LMFDB - Embedded newform 361.2.k.a.4.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [361,2,Mod(4,361)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(361, base_ring=CyclotomicField(342)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("361.4"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 361 = 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	361.k (of order $171$, degree $108$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.88259951297$
Analytic rank:	$0$
Dimension:	$3348$
Relative dimension:	$31$ over $\Q(\zeta_{171})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{171}]$

Embedding invariants

Embedding label			4.14
Character	$\chi$	$=$	361.4
Dual form			361.2.k.a.271.14

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.495679 - 0.00910759i) q^{2} +(2.27739 - 1.51792i) q^{3} +(-1.75304 - 0.0644421i) q^{4} +(-0.130251 - 0.269563i) q^{5} +(-1.14268 + 0.731660i) q^{6} +(4.23959 - 1.72197i) q^{7} +(1.85838 + 0.102529i) q^{8} +(1.72799 - 4.14479i) q^{9} +(0.0621075 + 0.134803i) q^{10} +(-0.490821 + 1.56924i) q^{11} +(-4.09016 + 2.51421i) q^{12} +(-3.73488 + 0.909376i) q^{13} +(-2.11716 + 0.814934i) q^{14} +(-0.705806 - 0.416188i) q^{15} +(2.57874 + 0.189848i) q^{16} +(-3.23130 - 5.15008i) q^{17} +(-0.894278 + 2.03875i) q^{18} +(-0.754771 + 4.29305i) q^{19} +(0.210963 + 0.480947i) q^{20} +(7.04137 - 10.3570i) q^{21} +(0.257582 - 0.773371i) q^{22} +(6.83679 - 3.38130i) q^{23} +(4.38787 - 2.58737i) q^{24} +(3.05148 - 3.84710i) q^{25} +(1.85959 - 0.416743i) q^{26} +(-0.782091 - 4.00387i) q^{27} +(-7.54312 + 2.74547i) q^{28} +(-3.25463 - 1.05089i) q^{29} +(0.346063 + 0.212724i) q^{30} +(-3.05211 + 2.65809i) q^{31} +(-4.98321 - 0.459047i) q^{32} +(1.26420 + 4.31880i) q^{33} +(1.55478 + 2.58222i) q^{34} +(-1.01639 - 0.918548i) q^{35} +(-3.29633 + 7.15461i) q^{36} +(0.0139183 + 0.0151193i) q^{37} +(0.413224 - 2.12110i) q^{38} +(-7.12541 + 7.74026i) q^{39} +(-0.214417 - 0.514303i) q^{40} +(0.0604888 + 0.171065i) q^{41} +(-3.58459 + 5.06960i) q^{42} +(4.94134 + 6.98843i) q^{43} +(0.961553 - 2.71931i) q^{44} +(-1.34235 + 0.0740597i) q^{45} +(-3.41965 + 1.61377i) q^{46} +(-3.90259 - 2.02018i) q^{47} +(6.16097 - 3.48198i) q^{48} +(9.99148 - 9.71986i) q^{49} +(-1.54759 + 1.87914i) q^{50} +(-15.1763 - 6.82386i) q^{51} +(6.60598 - 1.35348i) q^{52} +(0.550110 + 11.9688i) q^{53} +(0.351200 + 1.99176i) q^{54} +(0.486939 - 0.0720878i) q^{55} +(8.05531 - 2.76539i) q^{56} +(4.79761 + 10.9226i) q^{57} +(1.60368 + 0.550545i) q^{58} +(-0.327382 - 0.0608322i) q^{59} +(1.21048 + 0.775076i) q^{60} +(-0.494467 + 4.12097i) q^{61} +(1.53708 - 1.28976i) q^{62} +(0.188756 - 20.5478i) q^{63} +(-2.67417 - 0.295977i) q^{64} +(0.731605 + 0.888338i) q^{65} +(-0.587303 - 2.15225i) q^{66} +(-1.77181 + 7.57918i) q^{67} +(5.33270 + 9.23650i) q^{68} +(10.4375 - 18.0782i) q^{69} +(0.495437 + 0.464562i) q^{70} +(1.39605 + 11.6349i) q^{71} +(3.63622 - 7.52541i) q^{72} +(-4.22537 + 7.98211i) q^{73} +(-0.00676133 - 0.00762111i) q^{74} +(1.10980 - 13.3932i) q^{75} +(1.59979 - 7.47724i) q^{76} +(0.621313 + 7.49814i) q^{77} +(3.60241 - 3.77179i) q^{78} +(10.9404 - 1.00782i) q^{79} +(-0.284707 - 0.719861i) q^{80} +(1.62341 + 1.63840i) q^{81} +(-0.0284251 - 0.0853442i) q^{82} +(-5.10658 - 1.44400i) q^{83} +(-13.0112 + 17.7024i) q^{84} +(-0.967391 + 1.54184i) q^{85} +(-2.38567 - 3.50902i) q^{86} +(-9.00723 + 2.54700i) q^{87} +(-1.07302 + 2.86592i) q^{88} +(-6.47300 - 12.2281i) q^{89} +(0.666051 - 0.0244842i) q^{90} +(-14.2685 + 10.2868i) q^{91} +(-12.2030 + 5.48695i) q^{92} +(-2.91607 + 10.6864i) q^{93} +(1.91603 + 1.03691i) q^{94} +(1.25556 - 0.355715i) q^{95} +(-12.0455 + 6.51870i) q^{96} +(1.21441 + 5.19482i) q^{97} +(-5.04109 + 4.72693i) q^{98} +(5.65605 + 4.74599i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3348 q - 108 q^{2} - 111 q^{3} - 114 q^{4} - 108 q^{5} - 117 q^{6} - 111 q^{7} - 120 q^{8} - 117 q^{9} - 123 q^{10} - 111 q^{11} - 117 q^{12} - 111 q^{13} - 111 q^{14} - 117 q^{15} - 96 q^{16} - 3 q^{17}+ \cdots - 123 q^{99}+O(q^{100}) $ 3348 * q - 108 * q^2 - 111 * q^3 - 114 * q^4 - 108 * q^5 - 117 * q^6 - 111 * q^7 - 120 * q^8 - 117 * q^9 - 123 * q^10 - 111 * q^11 - 117 * q^12 - 111 * q^13 - 111 * q^14 - 117 * q^15 - 96 * q^16 - 3 * q^17 - 108 * q^18 - 102 * q^19 - 132 * q^20 - 114 * q^21 - 120 * q^23 - 129 * q^24 - 114 * q^25 - 105 * q^26 - 63 * q^27 - 120 * q^28 - 111 * q^29 - 90 * q^30 - 123 * q^31 - 123 * q^32 + 9 * q^33 - 114 * q^34 - 120 * q^35 - 90 * q^36 - 114 * q^37 - 42 * q^38 - 126 * q^39 - 114 * q^40 - 135 * q^41 - 111 * q^42 + 3 * q^43 - 123 * q^44 - 84 * q^45 - 96 * q^46 - 111 * q^47 + 516 * q^48 - 24 * q^49 - 99 * q^50 - 117 * q^51 - 129 * q^52 - 111 * q^53 + 483 * q^54 - 132 * q^55 - 108 * q^56 - 138 * q^57 - 174 * q^58 - 126 * q^59 - 108 * q^60 - 102 * q^61 - 102 * q^62 - 126 * q^63 + 6 * q^64 - 102 * q^65 - 105 * q^66 - 84 * q^67 - 12 * q^68 + 411 * q^69 + 351 * q^70 - 108 * q^71 - 102 * q^72 - 102 * q^73 - 15 * q^74 - 144 * q^75 - 150 * q^76 - 162 * q^77 - 129 * q^78 - 75 * q^79 - 117 * q^80 - 120 * q^81 - 60 * q^82 - 90 * q^83 - 117 * q^84 - 114 * q^85 + 888 * q^86 - 63 * q^87 - 123 * q^88 - 102 * q^89 + 894 * q^90 - 15 * q^91 - 156 * q^92 - 123 * q^93 - 132 * q^94 + 75 * q^95 - 276 * q^96 - 132 * q^97 - 105 * q^98 - 123 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/361\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{171}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.495679	−	0.00910759i	−0.350498	−	0.00644004i	−0.157163	−	0.987573i	$-0.550235\pi$
$2$	−0.495679	−	0.00910759i	−0.350498	−	0.00644004i	−0.193335	+	0.981133i	$0.561931\pi$
$3$	2.27739	−	1.51792i	1.31485	−	0.876372i	0.317438	−	0.948279i	$-0.397177\pi$
$3$	2.27739	−	1.51792i	1.31485	−	0.876372i	0.997411	+	0.0719067i	$0.0229084\pi$
$4$	−1.75304	−	0.0644421i	−0.876518	−	0.0322211i
$5$	−0.130251	−	0.269563i	−0.0582499	−	0.120552i	0.869254	−	0.494366i	$-0.164600\pi$
$5$	−0.130251	−	0.269563i	−0.0582499	−	0.120552i	−0.927504	+	0.373814i	$0.878050\pi$
$6$	−1.14268	+	0.731660i	−0.466496	+	0.298699i
$7$	4.23959	−	1.72197i	1.60242	−	0.650845i	0.612240	−	0.790672i	$-0.290269\pi$
$7$	4.23959	−	1.72197i	1.60242	−	0.650845i	0.990176	+	0.139827i	$0.0446547\pi$
$8$	1.85838	+	0.102529i	0.657035	+	0.0362496i
$9$	1.72799	−	4.14479i	0.575997	−	1.38160i
$10$	0.0621075	+	0.134803i	0.0196401	+	0.0426284i
$11$	−0.490821	+	1.56924i	−0.147988	+	0.473145i	−0.998614	−	0.0526264i	$-0.983241\pi$
$11$	−0.490821	+	1.56924i	−0.147988	+	0.473145i	0.850626	+	0.525771i	$0.176223\pi$
$12$	−4.09016	+	2.51421i	−1.18073	+	0.725790i
$13$	−3.73488	+	0.909376i	−1.03587	+	0.252215i	−0.718091	−	0.695949i	$-0.754984\pi$
$13$	−3.73488	+	0.909376i	−1.03587	+	0.252215i	−0.317779	+	0.948165i	$0.602937\pi$
$14$	−2.11716	+	0.814934i	−0.565835	+	0.217800i
$15$	−0.705806	−	0.416188i	−0.182238	−	0.107459i
$16$	2.57874	+	0.189848i	0.644686	+	0.0474619i
$17$	−3.23130	−	5.15008i	−0.783705	−	1.24908i	−0.964115	−	0.265486i	$-0.914468\pi$
$17$	−3.23130	−	5.15008i	−0.783705	−	1.24908i	0.180410	−	0.983592i	$-0.442258\pi$
$18$	−0.894278	+	2.03875i	−0.210783	+	0.480538i
$19$	−0.754771	+	4.29305i	−0.173156	+	0.984894i
$19$	−0.754771	+	4.29305i	−0.173156	+	0.984894i
$20$	0.210963	+	0.480947i	0.0471727	+	0.107543i
$21$	7.04137	−	10.3570i	1.53655	−	2.26008i
$22$	0.257582	−	0.773371i	0.0549167	−	0.164883i
$23$	6.83679	−	3.38130i	1.42557	−	0.705049i	0.443977	−	0.896038i	$-0.353567\pi$
$23$	6.83679	−	3.38130i	1.42557	−	0.705049i	0.981592	+	0.190989i	$0.0611695\pi$
$24$	4.38787	−	2.58737i	0.895671	−	0.528145i
$25$	3.05148	−	3.84710i	0.610296	−	0.769421i
$26$	1.85959	−	0.416743i	0.364695	−	0.0817300i
$27$	−0.782091	−	4.00387i	−0.150513	−	0.770545i
$28$	−7.54312	+	2.74547i	−1.42552	+	0.518846i
$29$	−3.25463	−	1.05089i	−0.604370	−	0.195145i	−0.0108195	−	0.999941i	$-0.503444\pi$
$29$	−3.25463	−	1.05089i	−0.604370	−	0.195145i	−0.593551	+	0.804796i	$0.702274\pi$
$30$	0.346063	+	0.212724i	0.0631821	+	0.0388379i
$31$	−3.05211	+	2.65809i	−0.548176	+	0.477407i	−0.885924	−	0.463830i	$-0.846475\pi$
$31$	−3.05211	+	2.65809i	−0.548176	+	0.477407i	0.337749	+	0.941236i	$0.390335\pi$
$32$	−4.98321	−	0.459047i	−0.880916	−	0.0811488i
$33$	1.26420	+	4.31880i	0.220069	+	0.751807i
$34$	1.55478	+	2.58222i	0.266643	+	0.442846i
$35$	−1.01639	−	0.918548i	−0.171801	−	0.155263i
$36$	−3.29633	+	7.15461i	−0.549388	+	1.19243i
$37$	0.0139183	+	0.0151193i	0.00228816	+	0.00248561i	0.736867	−	0.676038i	$-0.236304\pi$
$37$	0.0139183	+	0.0151193i	0.00228816	+	0.00248561i	−0.734579	+	0.678523i	$0.762620\pi$
$38$	0.413224	−	2.12110i	0.0670337	−	0.344088i
$39$	−7.12541	+	7.74026i	−1.14098	+	1.23943i
$40$	−0.214417	−	0.514303i	−0.0339022	−	0.0813185i
$41$	0.0604888	+	0.171065i	0.00944677	+	0.0267158i	0.947423	−	0.319982i	$-0.103677\pi$
$41$	0.0604888	+	0.171065i	0.00944677	+	0.0267158i	−0.937977	+	0.346698i	$0.887303\pi$
$42$	−3.58459	+	5.06960i	−0.553114	+	0.782257i
$43$	4.94134	+	6.98843i	0.753547	+	1.06573i	0.995437	+	0.0954218i	$0.0304200\pi$
$43$	4.94134	+	6.98843i	0.753547	+	1.06573i	−0.241889	+	0.970304i	$0.577767\pi$
$44$	0.961553	−	2.71931i	0.144960	−	0.409951i
$45$	−1.34235	+	0.0740597i	−0.200106	+	0.0110402i
$46$	−3.41965	+	1.61377i	−0.504200	+	0.237938i
$47$	−3.90259	−	2.02018i	−0.569251	−	0.294674i	0.150834	−	0.988559i	$-0.451804\pi$
$47$	−3.90259	−	2.02018i	−0.569251	−	0.294674i	−0.720086	+	0.693885i	$0.755898\pi$
$48$	6.16097	−	3.48198i	0.889260	−	0.502580i
$49$	9.99148	−	9.71986i	1.42735	−	1.38855i
$50$	−1.54759	+	1.87914i	−0.218863	+	0.265750i
$51$	−15.1763	−	6.82386i	−2.12511	−	0.955532i
$52$	6.60598	−	1.35348i	0.916085	−	0.187694i
$53$	0.550110	+	11.9688i	0.0755634	+	1.64404i	0.605387	+	0.795931i	$0.293018\pi$
$53$	0.550110	+	11.9688i	0.0755634	+	1.64404i	−0.529824	+	0.848108i	$0.677742\pi$
$54$	0.351200	+	1.99176i	0.0477923	+	0.271044i
$55$	0.486939	−	0.0720878i	0.0656589	−	0.00972032i
$56$	8.05531	−	2.76539i	1.07644	−	0.369541i
$57$	4.79761	+	10.9226i	0.635459	+	1.44674i
$58$	1.60368	+	0.550545i	0.210574	+	0.0722901i
$59$	−0.327382	−	0.0608322i	−0.0426215	−	0.00791968i	0.161333	−	0.986900i	$-0.448421\pi$
$59$	−0.327382	−	0.0608322i	−0.0426215	−	0.00791968i	−0.203955	+	0.978980i	$0.565380\pi$
$60$	1.21048	+	0.775076i	0.156273	+	0.100062i
$61$	−0.494467	+	4.12097i	−0.0633101	+	0.527636i	0.925532	+	0.378669i	$0.123618\pi$
$61$	−0.494467	+	4.12097i	−0.0633101	+	0.527636i	−0.988842	+	0.148967i	$0.952405\pi$
$62$	1.53708	−	1.28976i	0.195209	−	0.163800i
$63$	0.188756	−	20.5478i	0.0237810	−	2.58878i
$64$	−2.67417	−	0.295977i	−0.334271	−	0.0369971i
$65$	0.731605	+	0.888338i	0.0907444	+	0.110185i
$66$	−0.587303	−	2.15225i	−0.0722920	−	0.264924i
$67$	−1.77181	+	7.57918i	−0.216460	+	0.925944i	0.748414	+	0.663232i	$0.230816\pi$
$67$	−1.77181	+	7.57918i	−0.216460	+	0.925944i	−0.964874	+	0.262712i	$0.915383\pi$
$68$	5.33270	+	9.23650i	0.646685	+	1.12009i
$69$	10.4375	−	18.0782i	1.25652	−	2.17636i
$70$	0.495437	+	0.464562i	0.0592161	+	0.0555258i
$71$	1.39605	+	11.6349i	0.165681	+	1.38081i	0.796388	+	0.604786i	$0.206741\pi$
$71$	1.39605	+	11.6349i	0.165681	+	1.38081i	−0.630707	+	0.776021i	$0.717235\pi$
$72$	3.63622	−	7.52541i	0.428533	−	0.886878i
$73$	−4.22537	+	7.98211i	−0.494543	+	0.934236i	0.503008	+	0.864282i	$0.332227\pi$
$73$	−4.22537	+	7.98211i	−0.494543	+	0.934236i	−0.997550	+	0.0699539i	$0.977715\pi$
$74$	−0.00676133	−	0.00762111i	−0.000785989	−	0.000885936i
$75$	1.10980	−	13.3932i	0.128148	−	1.54652i
$76$	1.59979	−	7.47724i	0.183509	−	0.857698i
$77$	0.621313	+	7.49814i	0.0708052	+	0.854492i
$78$	3.60241	−	3.77179i	0.407893	−	0.427071i
$79$	10.9404	−	1.00782i	1.23090	−	0.113389i	0.543336	−	0.839515i	$-0.317161\pi$
$79$	10.9404	−	1.00782i	1.23090	−	0.113389i	0.687561	+	0.726127i	$0.258682\pi$
$80$	−0.284707	−	0.719861i	−0.0318312	−	0.0804829i
$81$	1.62341	+	1.63840i	0.180379	+	0.182044i
$82$	−0.0284251	−	0.0853442i	−0.00313902	−	0.00942469i
$83$	−5.10658	−	1.44400i	−0.560520	−	0.158500i	−0.0199529	−	0.999801i	$-0.506352\pi$
$83$	−5.10658	−	1.44400i	−0.560520	−	0.158500i	−0.540567	+	0.841301i	$0.681790\pi$
$84$	−13.0112	+	17.7024i	−1.41964	+	1.93149i
$85$	−0.967391	+	1.54184i	−0.104928	+	0.167236i
$86$	−2.38567	−	3.50902i	−0.257254	−	0.378388i
$87$	−9.00723	+	2.54700i	−0.965676	+	0.273067i
$88$	−1.07302	+	2.86592i	−0.114385	+	0.305508i
$89$	−6.47300	−	12.2281i	−0.686136	−	1.29617i	−0.943985	−	0.329989i	$-0.892955\pi$
$89$	−6.47300	−	12.2281i	−0.686136	−	1.29617i	0.257848	−	0.966185i	$-0.416986\pi$
$90$	0.666051	−	0.0244842i	0.0702079	−	0.00258087i
$91$	−14.2685	+	10.2868i	−1.49574	+	1.07834i
$92$	−12.2030	+	5.48695i	−1.27225	+	0.572055i
$93$	−2.91607	+	10.6864i	−0.302383	+	1.10812i
$94$	1.91603	+	1.03691i	0.197624	+	0.106949i
$95$	1.25556	−	0.355715i	0.128817	−	0.0364956i
$96$	−12.0455	+	6.51870i	−1.22939	+	0.665312i
$97$	1.21441	+	5.19482i	0.123304	+	0.527454i	0.999005	+	0.0445997i	$0.0142012\pi$
$97$	1.21441	+	5.19482i	0.123304	+	0.527454i	−0.875700	+	0.482855i	$0.839600\pi$
$98$	−5.04109	+	4.72693i	−0.509227	+	0.477493i
$99$	5.65605	+	4.74599i	0.568455	+	0.476990i
$100$	−5.59727	+	6.54747i	−0.559727	+	0.654747i
$101$	−3.30842	−	4.33218i	−0.329200	−	0.431068i	0.600365	−	0.799726i	$-0.295022\pi$
$101$	−3.30842	−	4.33218i	−0.329200	−	0.431068i	−0.929565	+	0.368658i	$0.879817\pi$
$102$	7.46044	+	3.52067i	0.738694	+	0.348598i
$103$	16.7670	+	6.81015i	1.65210	+	0.671024i	0.996461	−	0.0840521i	$-0.0267862\pi$
$103$	16.7670	+	6.81015i	1.65210	+	0.671024i	0.655637	+	0.755076i	$0.272400\pi$
$104$	−7.03405	+	1.30703i	−0.689746	+	0.128165i
$105$	−3.70900	−	0.549090i	−0.361961	−	0.0535856i
$106$	−0.163671	−	5.93769i	−0.0158971	−	0.576719i
$107$	−1.39661	+	7.14985i	−0.135015	+	0.691202i	0.851082	+	0.525033i	$0.175947\pi$
$107$	−1.39661	+	7.14985i	−0.135015	+	0.691202i	−0.986097	+	0.166170i	$0.946860\pi$
$108$	1.11301	+	7.06932i	0.107100	+	0.680246i
$109$	0.669645	−	14.5695i	0.0641404	−	1.39551i	−0.682795	−	0.730610i	$-0.739236\pi$
$109$	0.669645	−	14.5695i	0.0641404	−	1.39551i	0.746935	−	0.664897i	$-0.231525\pi$
$110$	−0.242022	+	0.0312976i	−0.0230759	+	0.00298411i
$111$	0.0546474	+	0.0133057i	0.00518690	+	0.00126292i
$112$	11.2597	−	3.63566i	1.06395	−	0.343537i
$113$	6.01582	−	4.68230i	0.565920	−	0.440474i	−0.290410	−	0.956902i	$-0.593792\pi$
$113$	6.01582	−	4.68230i	0.565920	−	0.440474i	0.856330	+	0.516429i	$0.172739\pi$
$114$	−2.27860	−	5.45781i	−0.213410	−	0.511171i
$115$	−1.80197	−	1.40253i	−0.168034	−	0.130786i
$116$	5.63777	+	2.05198i	0.523454	+	0.190522i
$117$	−2.68467	+	17.0517i	−0.248198	+	1.57643i
$118$	0.161722	+	0.0331349i	0.0148878	+	0.00305032i
$119$	−22.5677	−	16.2700i	−2.06878	−	1.49147i
$120$	−1.26898	−	0.845800i	−0.115842	−	0.0772106i
$121$	6.81794	+	4.72745i	0.619812	+	0.429768i
$122$	0.282629	−	2.03817i	0.0255881	−	0.184528i
$123$	0.397419	+	0.297763i	0.0358341	+	0.0268484i
$124$	5.52176	−	4.46304i	0.495868	−	0.400793i
$125$	−2.89517	−	0.648823i	−0.258952	−	0.0580325i
$126$	−0.280703	+	10.1834i	−0.0250070	+	0.907208i
$127$	−1.32259	+	7.50076i	−0.117361	+	0.665584i	0.868194	+	0.496225i	$0.165281\pi$
$127$	−1.32259	+	7.50076i	−0.117361	+	0.665584i	−0.985554	+	0.169359i	$0.945830\pi$
$128$	11.2488	+	1.45466i	0.994263	+	0.128575i
$129$	21.8612	+	8.41479i	1.92477	+	0.740881i
$130$	−0.354551	−	0.446994i	−0.0310961	−	0.0392040i
$131$	1.05619	+	0.853684i	0.0922801	+	0.0745867i	0.673639	−	0.739060i	$-0.264730\pi$
$131$	1.05619	+	0.853684i	0.0922801	+	0.0745867i	−0.581359	+	0.813647i	$0.697479\pi$
$132$	−1.93787	−	7.65248i	−0.168670	−	0.666063i
$133$	4.19261	+	19.5005i	0.363545	+	1.69091i
$134$	0.947275	−	3.74070i	0.0818321	−	0.323148i
$135$	−0.977426	+	0.732329i	−0.0841234	+	0.0630288i
$136$	−5.47693	−	9.90209i	−0.469643	−	0.849097i
$137$	−14.7071	+	4.45213i	−1.25651	+	0.380371i	−0.846833	−	0.531858i	$-0.821494\pi$
$137$	−14.7071	+	4.45213i	−1.25651	+	0.380371i	−0.409679	+	0.912230i	$0.634359\pi$
$138$	−5.33828	+	8.86594i	−0.454425	+	0.754719i
$139$	−16.2898	−	4.28476i	−1.38169	−	0.363429i	−0.512829	−	0.858491i	$-0.671403\pi$
$139$	−16.2898	−	4.28476i	−1.38169	−	0.363429i	−0.868858	+	0.495062i	$0.835145\pi$
$140$	1.72257	+	1.67575i	0.145584	+	0.141626i
$141$	−11.9542	+	1.32309i	−1.00672	+	0.111424i
$142$	−0.586027	−	5.77989i	−0.0491783	−	0.485037i
$143$	0.406128	−	6.30728i	0.0339621	−	0.527441i
$144$	5.24293	−	10.3603i	0.436910	−	0.863359i
$145$	0.140638	+	1.01421i	0.0116793	+	0.0842253i
$146$	2.16713	−	3.91808i	0.179353	−	0.324263i
$147$	8.00047	−	37.3022i	0.659868	−	3.07663i
$148$	−0.0234250	−	0.0274017i	−0.00192552	−	0.00225240i
$149$	−0.0470122	−	5.11770i	−0.00385139	−	0.419258i	−0.979664	−	0.200647i	$-0.935695\pi$
$149$	−0.0470122	−	5.11770i	−0.00385139	−	0.419258i	0.975812	−	0.218611i	$-0.0701525\pi$
$150$	−0.672083	+	6.62865i	−0.0548753	+	0.541227i
$151$	5.88869	+	0.982649i	0.479215	+	0.0799668i	0.399272	−	0.916833i	$-0.369263\pi$
$151$	5.88869	+	0.982649i	0.479215	+	0.0799668i	0.0799431	+	0.996799i	$0.474526\pi$
$152$	−1.84281	+	7.90072i	−0.149472	+	0.640833i
$153$	−26.9297	+	4.49377i	−2.17713	+	0.363299i
$154$	−0.239682	−	3.72233i	−0.0193141	−	0.299954i
$155$	1.11406	+	0.476519i	0.0894836	+	0.0382749i
$156$	12.9899	−	13.1098i	1.04002	−	1.04962i
$157$	1.95206	+	0.965437i	0.155791	+	0.0770503i	0.519537	−	0.854448i	$-0.326105\pi$
$157$	1.95206	+	0.965437i	0.155791	+	0.0770503i	−0.363745	+	0.931498i	$0.618502\pi$
$158$	−5.43213	+	0.399914i	−0.432157	+	0.0318155i
$159$	19.4205	+	26.4225i	1.54014	+	2.09544i
$160$	0.525325	+	1.40308i	0.0415305	+	0.110923i
$161$	23.1627	−	26.1081i	1.82548	−	2.05761i
$162$	−0.789771	−	0.826904i	−0.0620502	−	0.0649677i
$163$	−2.69471	−	2.34682i	−0.211066	−	0.183817i	0.544756	−	0.838594i	$-0.316622\pi$
$163$	−2.69471	−	2.34682i	−0.211066	−	0.183817i	−0.755822	+	0.654777i	$0.772763\pi$
$164$	−0.0950153	−	0.303781i	−0.00741945	−	0.0237213i
$165$	0.999526	−	0.903307i	0.0778130	−	0.0703224i
$166$	2.51807	+	0.762271i	0.195440	+	0.0591637i
$167$	−4.28790	−	19.9923i	−0.331808	−	1.54705i	−0.763968	−	0.645254i	$-0.776752\pi$
$167$	−4.28790	−	19.9923i	−0.331808	−	1.54705i	0.432160	−	0.901797i	$-0.357751\pi$
$168$	14.1474	−	18.5252i	1.09150	−	1.42925i
$169$	1.57749	−	0.816588i	0.121345	−	0.0628145i
$170$	0.493558	−	0.755447i	0.0378542	−	0.0579401i
$171$	16.4896	+	10.5467i	1.26099	+	0.806529i
$172$	−8.21200	−	12.5694i	−0.626159	−	0.958407i
$173$	−4.36656	−	2.46784i	−0.331984	−	0.187626i	0.317006	−	0.948424i	$-0.397323\pi$
$173$	−4.36656	−	2.46784i	−0.331984	−	0.187626i	−0.648989	+	0.760798i	$0.724808\pi$
$174$	4.48789	−	1.18046i	0.340226	−	0.0894905i
$175$	6.31242	−	21.5647i	0.477174	−	1.63014i
$176$	−1.56362	+	3.95350i	−0.117862	+	0.298006i
$177$	−0.837914	+	0.358402i	−0.0629815	+	0.0269391i
$178$	3.09716	+	6.12016i	0.232142	+	0.458725i
$179$	−5.67336	+	3.93382i	−0.424047	+	0.294028i	−0.762540	−	0.646941i	$-0.776048\pi$
$179$	−5.67336	+	3.93382i	−0.424047	+	0.294028i	0.338493	+	0.940969i	$0.390083\pi$
$180$	2.35797	−	0.0433251i	0.175752	−	0.00322927i
$181$	−8.42628	+	0.154824i	−0.626321	+	0.0115080i	−0.330607	−	0.943769i	$-0.607253\pi$
$181$	−8.42628	+	0.154824i	−0.626321	+	0.0115080i	−0.295714	+	0.955277i	$0.595557\pi$
$182$	7.16627	−	4.96898i	0.531199	−	0.368325i
$183$	5.12921	+	10.1356i	0.379162	+	0.749245i
$184$	13.0520	−	5.58275i	0.962207	−	0.411566i
$185$	0.00226274	−	0.00572117i	0.000166360	−	0.000420629i
$186$	1.54276	−	5.27045i	0.113121	−	0.386448i
$187$	9.66772	−	2.54292i	0.706974	−	0.185957i
$188$	6.71119	+	3.79294i	0.489464	+	0.276629i
$189$	−10.2103	−	15.6280i	−0.742690	−	1.13677i
$190$	−0.625593	+	0.164885i	−0.0453853	+	0.0119620i
$191$	9.28809	−	14.2165i	0.672063	−	1.02867i	−0.324505	−	0.945884i	$-0.605198\pi$
$191$	9.28809	−	14.2165i	0.672063	−	1.02867i	0.996567	−	0.0827845i	$-0.0263813\pi$
$192$	−6.53938	+	3.38512i	−0.471939	+	0.244300i
$193$	−4.77602	+	6.25391i	−0.343785	+	0.450166i	−0.934102	−	0.357005i	$-0.883798\pi$
$193$	−4.77602	+	6.25391i	−0.343785	+	0.450166i	0.590317	+	0.807171i	$0.299003\pi$
$194$	−0.554644	−	2.58603i	−0.0398211	−	0.185666i
$195$	3.01457	+	0.912571i	0.215878	+	0.0653506i
$196$	−18.1418	+	16.3954i	−1.29584	+	1.17110i
$197$	−7.01836	−	22.4389i	−0.500037	−	1.59871i	−0.771480	−	0.636254i	$-0.780483\pi$
$197$	−7.01836	−	22.4389i	−0.500037	−	1.59871i	0.271443	−	0.962455i	$-0.412499\pi$
$198$	−2.76036	−	2.40400i	−0.196170	−	0.170845i
$199$	5.86031	+	6.13585i	0.415427	+	0.434959i	0.897394	−	0.441230i	$-0.145458\pi$
$199$	5.86031	+	6.13585i	0.415427	+	0.434959i	−0.481967	+	0.876189i	$0.660078\pi$
$200$	6.06524	−	6.83650i	0.428877	−	0.483414i
$201$	7.46951	+	19.9502i	0.526859	+	1.40718i
$202$	1.60046	+	2.17750i	0.112608	+	0.153209i
$203$	−15.6079	+	1.14906i	−1.09546	+	0.0806480i
$204$	26.1649	+	12.9405i	1.83191	+	0.906014i
$205$	0.0382340	−	0.0385868i	0.00267038	−	0.00269502i
$206$	−8.24901	−	3.52836i	−0.574736	−	0.245832i
$207$	−2.20086	−	34.1799i	−0.152970	−	2.37567i
$208$	−9.80395	+	1.63599i	−0.679782	+	0.113435i
$209$	−6.36639	−	3.29154i	−0.440372	−	0.227681i
$210$	1.83347	+	0.305952i	0.126522	+	0.0211127i
$211$	1.29472	−	12.7696i	0.0891322	−	0.879097i	−0.847971	−	0.530043i	$-0.822176\pi$
$211$	1.29472	−	12.7696i	0.0891322	−	0.879097i	0.937103	−	0.349054i	$-0.113497\pi$
$212$	−0.193068	−	21.0171i	−0.0132599	−	1.44346i
$213$	20.8402	+	24.3780i	1.42795	+	1.67036i
$214$	0.757387	−	3.53131i	0.0517739	−	0.241396i
$215$	1.24021	−	2.24225i	0.0845815	−	0.152920i
$216$	−1.04290	−	7.52088i	−0.0709606	−	0.511731i
$217$	−8.36256	+	16.5249i	−0.567688	+	1.12178i
$218$	−0.464622	+	7.21571i	−0.0314682	+	0.488710i
$219$	2.49341	+	24.5921i	0.168489	+	1.66178i
$220$	−0.858267	+	0.0949930i	−0.0578644	+	0.00640443i
$221$	16.7519	+	16.2965i	1.12685	+	1.09622i
$222$	−0.0269664	−	0.00709304i	−0.00180987	−	0.000476054i
$223$	4.39802	−	7.30433i	0.294513	−	0.489134i	−0.673786	−	0.738926i	$-0.735333\pi$
$223$	4.39802	−	7.30433i	0.294513	−	0.489134i	0.968299	+	0.249792i	$0.0803624\pi$
$224$	−21.9173	+	6.63479i	−1.46441	+	0.443305i
$225$	−10.6725	−	19.2955i	−0.711501	−	1.28637i
$226$	−3.02456	+	2.26613i	−0.201191	+	0.150741i
$227$	−1.71113	+	6.75712i	−0.113572	+	0.448486i	−0.999894	−	0.0145844i	$-0.995357\pi$
$227$	−1.71113	+	6.75712i	−0.113572	+	0.448486i	0.886322	+	0.463070i	$0.153252\pi$
$228$	−7.70651	−	19.4569i	−0.510376	−	1.28857i
$229$	2.69945	+	10.6599i	0.178385	+	0.704425i	0.992344	+	0.123503i	$0.0394129\pi$
$229$	2.69945	+	10.6599i	0.178385	+	0.704425i	−0.813960	+	0.580921i	$0.802692\pi$
$230$	0.880424	+	0.711615i	0.0580535	+	0.0469225i
$231$	12.7966	+	16.1330i	0.841951	+	1.06148i
$232$	−5.94059	−	2.28664i	−0.390019	−	0.150125i
$233$	−11.2952	−	1.46066i	−0.739973	−	0.0956910i	−0.250997	−	0.967988i	$-0.580758\pi$
$233$	−11.2952	−	1.46066i	−0.739973	−	0.0956910i	−0.488977	+	0.872297i	$0.662630\pi$
$234$	1.48603	−	8.42772i	0.0971451	−	0.550937i
$235$	−0.0362511	+	1.31512i	−0.00236476	+	0.0857892i
$236$	0.569992	+	0.127738i	0.0371033	+	0.00831505i
$237$	23.3858	−	18.9019i	1.51907	−	1.22781i
$238$	11.0382	+	8.27025i	0.715497	+	0.536081i
$239$	0.969390	−	6.99073i	0.0627046	−	0.452193i	−0.933020	−	0.359824i	$-0.882837\pi$
$239$	0.969390	−	6.99073i	0.0627046	−	0.452193i	0.995725	−	0.0923690i	$-0.0294439\pi$
$240$	−1.74108	−	1.20724i	−0.112386	−	0.0779269i
$241$	−16.8090	−	11.2035i	−1.08277	−	0.721684i	−0.120204	−	0.992749i	$-0.538355\pi$
$241$	−16.8090	−	11.2035i	−1.08277	−	0.721684i	−0.962561	+	0.271066i	$0.912624\pi$
$242$	−3.33645	−	2.40539i	−0.214475	−	0.154625i
$243$	18.1736	+	3.72355i	1.16584	+	0.238866i
$244$	1.13238	−	7.19234i	0.0724934	−	0.460442i
$245$	−3.92151	−	1.42731i	−0.250536	−	0.0911877i
$246$	−0.194281	−	0.151215i	−0.0123869	−	0.00964109i
$247$	−1.08502	−	16.7204i	−0.0690381	−	1.06390i
$248$	−5.94451	+	4.62680i	−0.377477	+	0.293802i
$249$	−13.8215	+	4.46283i	−0.875904	+	0.282821i
$250$	1.42917	+	0.347976i	0.0903884	+	0.0220079i
$251$	−11.7514	+	1.51966i	−0.741743	+	0.0959199i	−0.489815	−	0.871826i	$-0.662936\pi$
$251$	−11.7514	+	1.51966i	−0.741743	+	0.0959199i	−0.251928	+	0.967746i	$0.581064\pi$
$252$	−1.65504	+	36.0088i	−0.104258	+	2.26834i
$253$	1.95044	+	12.3882i	0.122623	+	0.778840i
$254$	0.723892	−	3.70592i	0.0454210	−	0.232530i
$255$	0.137267	+	4.97979i	0.00859598	+	0.311846i
$256$	−0.239570	−	0.0354666i	−0.0149731	−	0.00221666i
$257$	10.7765	−	2.00243i	0.672220	−	0.124908i	0.164430	−	0.986389i	$-0.447422\pi$
$257$	10.7765	−	2.00243i	0.672220	−	0.124908i	0.507790	+	0.861481i	$0.330463\pi$
$258$	−10.7595	−	4.37014i	−0.669858	−	0.272073i
$259$	0.0850432	+	0.0401329i	0.00528433	+	0.00249374i
$260$	−1.22528	−	1.60443i	−0.0759888	−	0.0995028i
$261$	−9.97969	+	11.6739i	−0.617727	+	0.722593i
$262$	−0.515759	−	0.432773i	−0.0318637	−	0.0267368i
$263$	−10.1444	+	9.51222i	−0.625531	+	0.586548i	−0.930715	−	0.365745i	$-0.880814\pi$
$263$	−10.1444	+	9.51222i	−0.625531	+	0.586548i	0.305184	+	0.952293i	$0.401282\pi$
$264$	1.90655	+	8.15558i	0.117340	+	0.501941i
$265$	3.15469	−	1.70723i	0.193791	−	0.104874i
$266$	−1.90058	−	9.70418i	−0.116532	−	0.595001i
$267$	−33.3028	−	18.0226i	−2.03810	−	1.10296i
$268$	3.59446	−	13.1724i	0.219566	−	0.804632i
$269$	−26.8097	+	12.0547i	−1.63462	+	0.734986i	−0.999305	−	0.0372703i	$-0.988134\pi$
$269$	−26.8097	+	12.0547i	−1.63462	+	0.734986i	−0.635311	+	0.772257i	$0.719128\pi$
$270$	0.491159	−	0.354098i	0.0298910	−	0.0215497i
$271$	19.4817	−	0.716155i	1.18343	−	0.0435033i	0.562112	−	0.827061i	$-0.309989\pi$
$271$	19.4817	−	0.716155i	1.18343	−	0.0435033i	0.621319	+	0.783558i	$0.286597\pi$
$272$	−7.35496	−	13.8942i	−0.445960	−	0.842459i
$273$	−16.8803	+	45.0853i	−1.02164	+	2.72869i
$274$	7.33055	−	2.07288i	0.442855	−	0.125227i
$275$	4.53931	+	6.67676i	0.273731	+	0.402624i
$276$	−19.4623	+	31.0192i	−1.17149	+	1.86713i
$277$	19.4343	−	26.4413i	1.16770	−	1.58871i	0.448718	−	0.893674i	$-0.351881\pi$
$277$	19.4343	−	26.4413i	1.16770	−	1.58871i	0.718978	−	0.695033i	$-0.244610\pi$
$278$	8.03551	+	2.27223i	0.481938	+	0.136279i
$279$	5.74320	+	17.2435i	0.343836	+	1.03234i
$280$	−1.79466	−	1.81122i	−0.107251	−	0.108241i
$281$	7.41562	+	18.7498i	0.442379	+	1.11852i	0.964132	+	0.265425i	$0.0855122\pi$
$281$	7.41562	+	18.7498i	0.442379	+	1.11852i	−0.521753	+	0.853097i	$0.674722\pi$
$282$	5.93749	−	0.546954i	0.353572	−	0.0325706i
$283$	−7.76298	+	8.12798i	−0.461461	+	0.483158i	−0.912344	−	0.409425i	$-0.865729\pi$
$283$	−7.76298	+	8.12798i	−0.461461	+	0.483158i	0.450882	+	0.892583i	$0.351109\pi$
$284$	−1.69755	−	20.4863i	−0.100731	−	1.21564i
$285$	2.31944	−	2.71594i	0.137392	−	0.160878i
$286$	−0.258753	+	3.12269i	−0.0153004	+	0.184648i
$287$	0.551017	+	0.621085i	0.0325255	+	0.0366615i
$288$	−10.5136	+	19.8611i	−0.619520	+	1.17033i
$289$	−8.68592	+	17.9761i	−0.510936	+	1.05742i
$290$	−0.0604743	−	0.504002i	−0.00355117	−	0.0295960i
$291$	10.6510	+	9.98724i	0.624373	+	0.585463i
$292$	7.92161	−	13.7206i	0.463577	−	0.802939i
$293$	−7.10072	−	12.2988i	−0.414828	−	0.718504i	0.580582	−	0.814202i	$-0.302825\pi$
$293$	−7.10072	−	12.2988i	−0.414828	−	0.718504i	−0.995410	+	0.0956978i	$0.969492\pi$
$294$	−4.30540	+	18.4170i	−0.251096	+	1.07410i
$295$	0.0262436	+	0.0961735i	0.00152796	+	0.00559944i
$296$	0.0243153	+	0.0295245i	0.00141330	+	0.00171608i
$297$	6.66691	+	0.737893i	0.386853	+	0.0428169i
$298$	−0.0233069	+	2.53716i	−0.00135013	+	0.146974i
$299$	−22.4597	+	18.8460i	−1.29888	+	1.08989i
$300$	−2.80860	+	23.4073i	−0.162155	+	1.35142i
$301$	32.9832	+	21.1192i	1.90112	+	1.21729i
$302$	−2.90995	−	0.540710i	−0.167449	−	0.0311144i
$303$	−14.1105	−	4.84412i	−0.810624	−	0.278288i
$304$	−2.76139	+	10.9274i	−0.158376	+	0.626729i
$305$	1.17526	−	0.403469i	0.0672954	−	0.0231026i
$306$	13.3894	−	1.98220i	0.765421	−	0.113315i
$307$	0.308483	+	1.74950i	0.0176061	+	0.0998490i	0.992345	−	0.123500i	$-0.0394120\pi$
$307$	0.308483	+	1.74950i	0.0176061	+	0.0998490i	−0.974738	+	0.223349i	$0.928301\pi$
$308$	−0.605988	−	13.1845i	−0.0345294	−	0.751259i
$309$	48.5221	−	9.94158i	2.76033	−	0.565557i
$310$	−0.547877	−	0.246347i	−0.0311173	−	0.0139916i
$311$	22.3379	−	27.1234i	1.26666	−	1.53803i	0.566438	−	0.824104i	$-0.308321\pi$
$311$	22.3379	−	27.1234i	1.26666	−	1.53803i	0.700226	−	0.713921i	$-0.253083\pi$
$312$	−14.0353	+	13.6537i	−0.794592	+	0.772991i
$313$	−17.0787	+	9.65231i	−0.965345	+	0.545581i	−0.892151	−	0.451737i	$-0.850805\pi$
$313$	−17.0787	+	9.65231i	−0.965345	+	0.545581i	−0.0731941	+	0.997318i	$0.523319\pi$
$314$	−0.958802	−	0.496326i	−0.0541084	−	0.0280093i
$315$	−5.56350	+	2.62548i	−0.313468	+	0.147929i
$316$	−19.2439	+	1.06172i	−1.08256	+	0.0597263i
$317$	−0.544444	+	1.53971i	−0.0305790	+	0.0864787i	−0.957092	−	0.289784i	$-0.906417\pi$
$317$	−0.544444	+	1.53971i	−0.0305790	+	0.0864787i	0.926513	+	0.376262i	$0.122791\pi$
$318$	−9.38568	−	13.2740i	−0.526323	−	0.744367i
$319$	3.24654	−	4.59152i	0.181772	−	0.257076i
$320$	0.268528	+	0.759407i	0.0150112	+	0.0424521i
$321$	7.67230	+	18.4029i	0.428226	+	1.02715i
$322$	−11.7191	+	12.7303i	−0.653077	+	0.709431i
$323$	24.5485	−	9.98501i	1.36591	−	0.555581i
$324$	−2.74032	−	2.97678i	−0.152240	−	0.165377i
$325$	−7.89845	+	17.1434i	−0.438127	+	0.950946i
$326$	1.31434	+	1.18781i	0.0727944	+	0.0657869i
$327$	−20.5904	−	34.1969i	−1.13865	−	1.89109i
$328$	0.0948718	+	0.324105i	0.00523842	+	0.0178957i
$329$	−20.0241	−	1.84459i	−1.10396	−	0.101696i
$330$	−0.503671	+	0.438647i	−0.0277262	+	0.0241467i
$331$	−17.1649	−	10.5512i	−0.943468	−	0.579948i	−0.0356738	−	0.999363i	$-0.511358\pi$
$331$	−17.1649	−	10.5512i	−0.943468	−	0.579948i	−0.907794	+	0.419416i	$0.862235\pi$
$332$	8.85896	+	2.86047i	0.486199	+	0.156989i
$333$	0.0867173	−	0.0315625i	0.00475208	−	0.00172962i
$334$	1.94334	+	9.94882i	0.106335	+	0.544375i
$335$	2.27384	−	0.509580i	0.124233	−	0.0278413i
$336$	20.1241	−	25.3712i	1.09786	−	1.38411i
$337$	−4.26279	+	2.51361i	−0.232209	+	0.136925i	−0.619404	−	0.785073i	$-0.712625\pi$
$337$	−4.26279	+	2.51361i	−0.232209	+	0.136925i	0.387194	+	0.921998i	$0.373444\pi$
$338$	−0.789364	+	0.390399i	−0.0429357	+	0.0212349i
$339$	6.59298	−	19.7949i	0.358081	−	1.07511i
$340$	1.79523	−	2.64056i	0.0973600	−	0.143204i
$341$	−2.67315	−	6.09416i	−0.144759	−	0.330017i
$342$	−8.07748	−	5.37797i	−0.436780	−	0.290808i
$343$	12.7555	−	29.0796i	0.688732	−	1.57015i
$344$	8.46635	+	13.4938i	0.456475	+	0.727535i
$345$	−6.23270	−	0.458852i	−0.335557	−	0.0247038i
$346$	2.14194	+	1.26302i	0.115151	+	0.0679006i
$347$	−2.67305	+	1.02890i	−0.143497	+	0.0552345i	−0.429910	−	0.902872i	$-0.641455\pi$
$347$	−2.67305	+	1.02890i	−0.143497	+	0.0552345i	0.286414	+	0.958106i	$0.407537\pi$
$348$	15.9541	−	3.88454i	0.855230	−	0.208233i
$349$	−2.34800	+	1.44331i	−0.125686	+	0.0772587i	−0.585089	−	0.810969i	$-0.698940\pi$
$349$	−2.34800	+	1.44331i	−0.125686	+	0.0772587i	0.459403	+	0.888228i	$0.348063\pi$
$350$	−3.32534	+	10.6317i	−0.177747	+	0.568288i
$351$	6.56204	+	14.2428i	0.350256	+	0.760222i
$352$	3.16622	−	7.59456i	0.168760	−	0.404792i
$353$	−4.75624	−	0.262409i	−0.253149	−	0.0139666i	−0.0719313	−	0.997410i	$-0.522916\pi$
$353$	−4.75624	−	0.262409i	−0.253149	−	0.0139666i	−0.181218	+	0.983443i	$0.558004\pi$
$354$	0.418601	−	0.170021i	0.0222484	−	0.00903651i
$355$	2.95450	−	1.89177i	0.156808	−	0.100405i
$356$	10.5594	+	21.8534i	0.559647	+	1.15823i
$357$	−76.0920	−	2.79717i	−4.02721	−	0.148042i
$358$	2.84800	−	1.89824i	0.150521	−	0.100325i
$359$	−8.74533	−	0.160686i	−0.461561	−	0.00848070i	−0.212906	−	0.977073i	$-0.568293\pi$
$359$	−8.74533	−	0.160686i	−0.461561	−	0.00848070i	−0.248655	+	0.968592i	$0.579989\pi$
$360$	−2.50219			−0.131877
$361$	−17.8606	−	6.48055i	−0.940034	−	0.341082i
$362$	4.17814			0.219598
$363$	22.7030	+	0.417143i	1.19160	+	0.0218943i
$364$	25.6760	−	17.1136i	1.34579	−	0.896994i
$365$	2.70204	+	0.0993278i	0.141431	+	0.00519905i
$366$	−2.45013	−	5.07072i	−0.128070	−	0.265051i
$367$	9.34040	−	5.98069i	0.487565	−	0.312190i	−0.272366	−	0.962194i	$-0.587806\pi$
$367$	9.34040	−	5.98069i	0.487565	−	0.312190i	0.759931	+	0.650004i	$0.225233\pi$
$368$	18.2723	−	7.42155i	0.952508	−	0.386875i
$369$	0.813552	+	0.0448849i	0.0423518	+	0.00233662i
$370$	−0.00117370	+	0.00281526i	−6.10177e−5	+	0.000146358i
$371$	22.9422	+	49.7955i	1.19110	+	2.58525i
$372$	5.80063	−	18.5457i	0.300749	−	0.961547i
$373$	11.5107	−	7.07563i	0.596004	−	0.366362i	−0.192588	−	0.981280i	$-0.561688\pi$
$373$	11.5107	−	7.07563i	0.596004	−	0.366362i	0.788591	+	0.614918i	$0.210811\pi$
$374$	−4.81525	+	1.17243i	−0.248991	+	0.0606247i
$375$	−7.57828	+	2.91702i	−0.391341	+	0.150634i
$376$	−7.04535	−	4.15439i	−0.363336	−	0.214246i
$377$	13.1113	+	0.965258i	0.675268	+	0.0497133i
$378$	4.91870	+	7.83948i	0.252991	+	0.403219i
$379$	10.9720	−	25.0135i	0.563592	−	1.28486i	−0.370833	−	0.928699i	$-0.620928\pi$
$379$	10.9720	−	25.0135i	0.563592	−	1.28486i	0.934425	−	0.356160i	$-0.115914\pi$
$380$	−2.22396	+	0.542670i	−0.114087	+	0.0278384i
$381$	8.37352	+	19.0897i	0.428988	+	0.977995i
$382$	−4.73339	+	6.96222i	−0.242181	+	0.356218i
$383$	−5.95303	+	17.8735i	−0.304185	+	0.913294i	0.679544	+	0.733635i	$0.262178\pi$
$383$	−5.95303	+	17.8735i	−0.304185	+	0.913294i	−0.983729	+	0.179659i	$0.942500\pi$
$384$	27.8259	−	13.7620i	1.41999	−	0.702288i
$385$	1.94029	−	1.14412i	0.0988864	−	0.0583098i
$386$	2.42433	−	3.05643i	0.123395	−	0.155568i
$387$	37.5042	−	8.40488i	1.90644	−	0.427244i
$388$	−1.79413	−	9.18497i	−0.0910834	−	0.466296i
$389$	29.4786	−	10.7293i	1.49463	−	0.543999i	0.539962	−	0.841689i	$-0.318438\pi$
$389$	29.4786	−	10.7293i	1.49463	−	0.543999i	0.954663	+	0.297690i	$0.0962162\pi$
$390$	−1.48595	−	0.479798i	−0.0752440	−	0.0242955i
$391$	−39.5057	−	24.2840i	−1.99789	−	1.22810i
$392$	19.5645	−	17.0387i	0.988157	−	0.860586i
$393$	3.70119	+	0.340949i	0.186700	+	0.0171986i
$394$	3.27449	+	11.1864i	0.164966	+	0.563564i
$395$	−1.69667	−	2.81787i	−0.0853688	−	0.141782i
$396$	−9.60942	−	8.68438i	−0.482891	−	0.436406i
$397$	−3.81963	+	8.29043i	−0.191702	+	0.416085i	−0.979942	−	0.199283i	$-0.936139\pi$
$397$	−3.81963	+	8.29043i	−0.191702	+	0.416085i	0.788240	+	0.615368i	$0.210992\pi$
$398$	−2.84895	−	3.09479i	−0.142805	−	0.155128i
$399$	39.1484	+	38.0461i	1.95987	+	1.90469i
$400$	8.59935	−	9.34138i	0.429968	−	0.467069i
$401$	−3.97038	−	9.52342i	−0.198271	−	0.475577i	0.792707	−	0.609603i	$-0.208671\pi$
$401$	−3.97038	−	9.52342i	−0.198271	−	0.475577i	−0.990978	+	0.134026i	$0.957209\pi$
$402$	−3.52078	−	9.95692i	−0.175601	−	0.496606i
$403$	8.98208	−	12.7032i	0.447429	−	0.632790i
$404$	5.52060	+	7.80766i	0.274660	+	0.388446i
$405$	0.230200	−	0.651014i	0.0114387	−	0.0323491i
$406$	7.74699	−	0.427413i	0.384477	−	0.0212122i
$407$	−0.0305574	+	0.0144204i	−0.00151467	+	0.000714791i
$408$	−27.5037	−	14.2373i	−1.36164	−	0.704853i
$409$	−30.0678	+	16.9933i	−1.48676	+	0.840267i	−0.999456	−	0.0329666i	$-0.989504\pi$
$409$	−30.0678	+	16.9933i	−1.48676	+	0.840267i	−0.487303	+	0.873233i	$0.662019\pi$
$410$	−0.0193032	+	0.0187785i	−0.000953319	+	0.000927403i
$411$	−26.7358	+	32.4634i	−1.31878	+	1.60130i
$412$	−28.9542	−	13.0189i	−1.42647	−	0.641397i
$413$	−1.49272	+	0.305840i	−0.0734519	+	0.0150494i
$414$	0.779623	+	16.9623i	0.0383164	+	0.833652i
$415$	0.275886	+	1.56463i	0.0135427	+	0.0768045i
$416$	19.0292	−	2.81713i	0.932981	−	0.138121i
$417$	−43.6022	+	14.9687i	−2.13521	+	0.733018i
$418$	3.12571	+	1.68953i	0.152883	+	0.0826377i
$419$	28.6136	+	9.82306i	1.39787	+	0.479888i	0.917694	−	0.397287i	$-0.130048\pi$
$419$	28.6136	+	9.82306i	1.39787	+	0.479888i	0.480171	+	0.877175i	$0.340575\pi$
$420$	6.46662	+	1.20159i	0.315539	+	0.0586315i
$421$	−17.9143	−	11.4706i	−0.873088	−	0.559041i	0.0245879	−	0.999698i	$-0.492173\pi$
$421$	−17.9143	−	11.4706i	−0.873088	−	0.559041i	−0.897676	+	0.440656i	$0.854746\pi$
$422$	−0.758066	+	6.31784i	−0.0369021	+	0.307548i
$423$	−15.1169	+	12.6846i	−0.735008	+	0.616745i
$424$	−0.204842	+	22.2989i	−0.00994802	+	1.08293i
$425$	−29.6731	−	3.28422i	−1.43936	−	0.159308i
$426$	−10.1080	−	12.2735i	−0.489735	−	0.594652i
$427$	4.99986	+	18.3227i	0.241960	+	0.886697i
$428$	2.90905	−	12.4439i	0.140614	−	0.601501i
$429$	−8.64905	−	14.9806i	−0.417580	−	0.723270i
$430$	−0.635167	+	1.10014i	−0.0306305	+	0.0530535i
$431$	16.2770	+	15.2627i	0.784037	+	0.735176i	0.968864	−	0.247595i	$-0.0796402\pi$
$431$	16.2770	+	15.2627i	0.784037	+	0.735176i	−0.184827	+	0.982771i	$0.559172\pi$
$432$	−1.25669	−	10.4734i	−0.0604624	−	0.503903i
$433$	7.50967	−	15.5418i	0.360892	−	0.746891i	−0.638857	−	0.769326i	$-0.720592\pi$
$433$	7.50967	−	15.5418i	0.360892	−	0.746891i	0.999748	+	0.0224353i	$0.00714197\pi$
$434$	4.29565	−	8.11487i	0.206198	−	0.389526i
$435$	1.85977	+	2.09626i	0.0891693	+	0.100508i
$436$	−2.11280	+	25.4977i	−0.101185	+	1.22112i
$437$	9.35588	+	31.9028i	0.447552	+	1.52612i
$438$	−1.01196	−	12.2125i	−0.0483532	−	0.583537i
$439$	0.443501	−	0.464353i	0.0211671	−	0.0221624i	−0.712489	−	0.701683i	$-0.752432\pi$
$439$	0.443501	−	0.464353i	0.0211671	−	0.0221624i	0.733656	+	0.679521i	$0.237812\pi$
$440$	0.912308	−	0.0840406i	0.0434926	−	0.00400648i
$441$	−23.0216	−	58.2084i	−1.09627	−	2.77183i
$442$	−8.15513	−	8.23039i	−0.387900	−	0.391480i
$443$	9.96938	+	29.9323i	0.473660	+	1.42213i	0.864948	+	0.501861i	$0.167351\pi$
$443$	9.96938	+	29.9323i	0.473660	+	1.42213i	−0.391289	+	0.920268i	$0.627971\pi$
$444$	−0.0949414	−	0.0268469i	−0.00450572	−	0.00127410i
$445$	−2.45312	+	3.33759i	−0.116289	+	0.158217i
$446$	−2.24653	+	3.58055i	−0.106376	+	0.169544i
$447$	−7.87533	−	11.5836i	−0.372490	−	0.547886i
$448$	−11.8470	+	3.35003i	−0.559720	+	0.158274i
$449$	−5.73834	+	15.3264i	−0.270809	+	0.723298i	0.728461	+	0.685087i	$0.240236\pi$
$449$	−5.73834	+	15.3264i	−0.270809	+	0.723298i	−0.999270	+	0.0382109i	$0.987834\pi$
$450$	5.11441	+	9.66158i	0.241096	+	0.455451i
$451$	−0.298132	+	0.0109594i	−0.0140385	+	0.000516059i
$452$	−10.8477	+	7.82056i	−0.510232	+	0.367848i
$453$	14.9024	−	6.70070i	0.700176	−	0.314826i
$454$	0.909715	−	3.33378i	0.0426950	−	0.156462i
$455$	4.63140	+	2.50639i	0.217123	+	0.117501i
$456$	7.79588	+	20.7902i	0.365075	+	0.973592i
$457$	−31.3918	+	16.9884i	−1.46845	+	0.794685i	−0.996226	−	0.0867946i	$-0.972338\pi$
$457$	−31.3918	+	16.9884i	−1.46845	+	0.794685i	−0.472223	+	0.881479i	$0.656548\pi$
$458$	−1.24097	−	5.30847i	−0.0579869	−	0.248048i
$459$	−18.0931	+	16.9655i	−0.844512	+	0.791883i
$460$	3.06853	+	2.57480i	0.143071	+	0.120051i
$461$	−9.52813	+	11.1456i	−0.443769	+	0.519104i	−0.936305	−	0.351188i	$-0.885778\pi$
$461$	−9.52813	+	11.1456i	−0.443769	+	0.519104i	0.492536	+	0.870292i	$0.336070\pi$
$462$	−6.19605	−	8.11336i	−0.288266	−	0.377468i
$463$	−34.3798	−	16.2242i	−1.59776	−	0.754003i	−0.598862	−	0.800852i	$-0.704380\pi$
$463$	−34.3798	−	16.2242i	−1.59776	−	0.754003i	−0.998902	+	0.0468490i	$0.985082\pi$
$464$	−8.19336	−	3.32786i	−0.380367	−	0.154492i
$465$	3.26047	−	0.605841i	0.151200	−	0.0280952i
$466$	5.58549	+	0.826891i	0.258743	+	0.0383050i
$467$	0.0163989	+	0.594923i	0.000758852	+	0.0275297i	0.999905	−	0.0137869i	$-0.00438863\pi$
$467$	0.0163989	+	0.594923i	0.000758852	+	0.0275297i	−0.999146	+	0.0413166i	$0.986845\pi$
$468$	5.80517	−	29.7192i	0.268344	−	1.37377i
$469$	5.53942	+	35.1836i	0.255786	+	1.62463i
$470$	0.0299465	−	0.651549i	0.00138133	−	0.0300537i
$471$	5.91105	−	0.764399i	0.272367	−	0.0352216i
$472$	−0.602162	−	0.146615i	−0.0277168	−	0.00674853i
$473$	−13.3919	+	4.32410i	−0.615759	+	0.198822i
$474$	−11.7640	+	9.15631i	−0.540339	+	0.420563i
$475$	14.2127	+	16.0039i	0.652122	+	0.734307i
$476$	38.5135	+	29.9762i	1.76526	+	1.37396i
$477$	50.5587	+	18.4019i	2.31492	+	0.842563i
$478$	−0.544175	+	3.45633i	−0.0248900	+	0.158089i
$479$	−40.2590	−	8.24856i	−1.83948	−	0.376886i	−0.850624	−	0.525774i	$-0.823776\pi$
$479$	−40.2590	−	8.24856i	−1.83948	−	0.376886i	−0.988854	+	0.148887i	$0.952431\pi$
$480$	3.32613	+	2.39795i	0.151816	+	0.109451i
$481$	−0.0657325	−	0.0438120i	−0.00299715	−	0.00199765i
$482$	8.22985	+	5.70645i	0.374859	+	0.259922i
$483$	13.1204	−	94.6174i	0.596998	−	4.30524i
$484$	−11.6474	−	8.72675i	−0.529429	−	0.396671i
$485$	1.24215	−	1.00399i	0.0564033	−	0.0455888i
$486$	−8.97438	−	2.01121i	−0.407086	−	0.0912302i
$487$	0.114780	−	4.16399i	0.00520116	−	0.188688i	−0.992558	−	0.121775i	$-0.961141\pi$
$487$	0.114780	−	4.16399i	0.00520116	−	0.188688i	0.997759	−	0.0669128i	$-0.0213149\pi$
$488$	−1.34143	+	7.60761i	−0.0607235	+	0.344380i
$489$	−9.69919	−	1.25427i	−0.438612	−	0.0567200i
$490$	1.93081	+	0.743205i	0.0872252	+	0.0335746i
$491$	−10.5407	−	13.2890i	−0.475694	−	0.599724i	0.485963	−	0.873980i	$-0.338469\pi$
$491$	−10.5407	−	13.2890i	−0.475694	−	0.599724i	−0.961657	+	0.274256i	$0.911569\pi$
$492$	−0.677502	−	0.547600i	−0.0305441	−	0.0246877i
$493$	5.10454	+	20.1574i	0.229897	+	0.907842i
$494$	0.385538	+	8.29785i	0.0173462	+	0.373338i
$495$	0.542638	−	2.14283i	0.0243898	−	0.0963130i
$496$	−8.37525	+	6.27509i	−0.376060	+	0.281760i
$497$	25.9537	+	46.9232i	1.16418	+	2.10479i
$498$	6.89169	−	2.08625i	0.308824	−	0.0934872i
$499$	6.62769	−	11.0074i	0.296696	−	0.492759i	−0.672153	−	0.740413i	$-0.734630\pi$
$499$	6.62769	−	11.0074i	0.296696	−	0.492759i	0.968849	+	0.247653i	$0.0796594\pi$
$500$	5.03352	+	1.32398i	0.225106	+	0.0592102i
$501$	−40.1119	−	39.0215i	−1.79207	−	1.74335i
$502$	5.83877	−	0.646235i	0.260597	−	0.0288429i
$503$	−1.93673	−	19.1016i	−0.0863544	−	0.851699i	−0.942330	−	0.334684i	$-0.891370\pi$
$503$	−1.93673	−	19.1016i	−0.0863544	−	0.851699i	0.855976	−	0.517016i	$-0.172957\pi$
$504$	2.45753	−	38.1662i	0.109467	−	1.70006i
$505$	−0.736870	+	1.45610i	−0.0327903	+	0.0647954i
$506$	−0.853963	−	6.15834i	−0.0379633	−	0.273771i
$507$	2.35303	−	4.25418i	0.104502	−	0.188935i
$508$	2.80190	−	13.0639i	0.124314	−	0.579615i
$509$	7.51945	+	8.79596i	0.333294	+	0.389874i	0.901333	−	0.433128i	$-0.142590\pi$
$509$	7.51945	+	8.79596i	0.333294	+	0.389874i	−0.568039	+	0.823002i	$0.692298\pi$
$510$	−0.0226865	−	2.46963i	−0.00100457	−	0.109357i
$511$	−4.16887	+	41.1169i	−0.184420	+	1.81890i
$512$	−22.2571	−	3.71406i	−0.983635	−	0.164140i
$513$	17.7791	−	0.335554i	0.784967	−	0.0148151i
$514$	−5.35993	+	0.894414i	−0.236416	+	0.0394509i
$515$	−0.348144	−	5.40678i	−0.0153411	−	0.238251i
$516$	−37.7812	−	16.1602i	−1.66323	−	0.711413i
$517$	5.08563	−	5.13257i	0.223666	−	0.225730i
$518$	−0.0417886	−	0.0206676i	−0.00183609	−	0.000908081i
$519$	−13.6903	+	1.00788i	−0.600939	+	0.0442412i
$520$	1.26852	+	1.72588i	0.0556281	+	0.0756847i
$521$	6.63852	+	17.7307i	0.290839	+	0.776796i	0.997593	+	0.0693370i	$0.0220884\pi$
$521$	6.63852	+	17.7307i	0.290839	+	0.776796i	−0.706754	+	0.707459i	$0.749841\pi$
$522$	5.05305	−	5.69560i	0.221166	−	0.249289i
$523$	−10.1394	−	10.6161i	−0.443365	−	0.464211i	0.463214	−	0.886246i	$-0.346696\pi$
$523$	−10.1394	−	10.6161i	−0.443365	−	0.464211i	−0.906580	+	0.422035i	$0.861316\pi$
$524$	−1.79653	−	1.56460i	−0.0784819	−	0.0683499i
$525$	−18.3577	−	58.6930i	−0.801198	−	2.56157i
$526$	5.11501	−	4.62262i	0.223025	−	0.201556i
$527$	23.5517	+	7.12955i	1.02593	+	0.310568i
$528$	2.44013	+	11.3771i	0.106193	+	0.495124i
$529$	21.3490	−	27.9552i	0.928216	−	1.21544i
$530$	−1.57926	+	0.817507i	−0.0685987	+	0.0355102i
$531$	−0.817850	+	1.25181i	−0.0354917	+	0.0543241i
$532$	−6.09313	−	34.4553i	−0.264171	−	1.49382i
$533$	−0.381481	−	0.583900i	−0.0165238	−	0.0252915i
$534$	16.3434	+	9.23672i	0.707246	+	0.399712i
$535$	2.10924	−	0.554799i	0.0911905	−	0.0239861i
$536$	−4.06977	+	13.9033i	−0.175787	+	0.600531i
$537$	−6.94921	+	17.5706i	−0.299880	+	0.758225i
$538$	13.3988	−	5.73108i	0.577663	−	0.247084i
$539$	10.3488	+	20.4498i	0.445754	+	0.880835i
$540$	1.76065	−	1.22081i	0.0757665	−	0.0525353i
$541$	25.9680	−	0.477135i	1.11645	−	0.0205136i	0.542985	−	0.839743i	$-0.317294\pi$
$541$	25.9680	−	0.477135i	1.11645	−	0.0205136i	0.573467	+	0.819229i	$0.305598\pi$
$542$	−9.66321	+	0.177551i	−0.415070	+	0.00762648i
$543$	−18.9549	+	13.1430i	−0.813432	+	0.564021i
$544$	13.7381	+	27.1473i	0.589017	+	1.16393i
$545$	−4.01462	+	1.71718i	−0.171968	+	0.0735558i
$546$	8.77784	−	22.1941i	0.375657	−	0.949820i
$547$	4.55355	−	15.5560i	0.194696	−	0.665127i	−0.802918	−	0.596089i	$-0.796721\pi$
$547$	4.55355	−	15.5560i	0.194696	−	0.665127i	0.997614	−	0.0690379i	$-0.0219929\pi$
$548$	26.0690	−	6.85699i	1.11361	−	0.292916i
$549$	16.2261	+	9.17046i	0.692514	+	0.391386i
$550$	−2.18923	−	3.35087i	−0.0933492	−	0.142882i
$551$	6.96802	−	13.1791i	0.296848	−	0.561450i
$552$	21.2503	−	32.5260i	0.904473	−	1.38440i
$553$	44.6476	−	23.1119i	1.89861	−	0.982818i
$554$	−9.87401	+	12.9294i	−0.419506	+	0.549319i
$555$	−0.00353115	−	0.0164640i	−0.000149889	−	0.000698857i
$556$	28.2806	+	8.56109i	1.19936	+	0.363071i
$557$	4.61459	−	4.17037i	0.195527	−	0.176704i	−0.566885	−	0.823797i	$-0.691852\pi$
$557$	4.61459	−	4.17037i	0.195527	−	0.176704i	0.762411	+	0.647093i	$0.224015\pi$
$558$	−2.68974	−	8.59956i	−0.113866	−	0.364049i
$559$	−24.8104	−	21.6074i	−1.04937	−	0.913897i
$560$	−2.44663	−	2.56166i	−0.103389	−	0.108250i
$561$	18.1572	−	20.4661i	0.766597	−	0.864078i
$562$	−3.50500	−	9.36144i	−0.147850	−	0.394889i
$563$	−4.15958	−	5.65931i	−0.175305	−	0.238512i	0.709238	−	0.704969i	$-0.249039\pi$
$563$	−4.15958	−	5.65931i	−0.175305	−	0.238512i	−0.884544	+	0.466457i	$0.845530\pi$
$564$	21.0414	−	1.54907i	0.886001	−	0.0652275i
$565$	−2.04574	−	1.01177i	−0.0860648	−	0.0425654i
$566$	3.92197	−	3.95817i	0.164853	−	0.166374i
$567$	9.70389	+	4.15065i	0.407525	+	0.174311i
$568$	1.40146	+	21.7651i	0.0588042	+	0.913245i
$569$	27.1332	−	4.52773i	1.13748	−	0.189813i	0.434265	−	0.900785i	$-0.357008\pi$
$569$	27.1332	−	4.52773i	1.13748	−	0.189813i	0.703219	+	0.710973i	$0.251745\pi$
$570$	−1.17443	+	1.32511i	−0.0491916	+	0.0555027i
$571$	34.8809	+	5.82059i	1.45972	+	0.243584i	0.840576	−	0.541693i	$-0.182217\pi$
$571$	34.8809	+	5.82059i	1.45972	+	0.243584i	0.619144	+	0.785278i	$0.287480\pi$
$572$	−1.11841	+	11.0307i	−0.0467631	+	0.461217i
$573$	−0.426929	−	46.4750i	−0.0178352	−	1.94152i
$574$	−0.267471	−	0.312877i	−0.0111640	−	0.0130593i
$575$	7.85412	−	36.6198i	0.327540	−	1.52715i
$576$	−5.84770	+	10.5724i	−0.243654	+	0.440517i
$577$	0.0245973	+	0.177383i	0.00102400	+	0.00738454i	0.991027	−	0.133660i	$-0.0426731\pi$
$577$	0.0245973	+	0.177383i	0.00102400	+	0.00738454i	−0.990003	+	0.141045i	$0.954954\pi$
$578$	4.46915	−	8.83127i	0.185892	−	0.367333i
$579$	−1.38389	+	21.4922i	−0.0575125	+	0.893185i
$580$	−0.181186	−	1.78700i	−0.00752332	−	0.0742013i
$581$	−24.1364	+	2.67141i	−1.00134	+	0.110829i
$582$	−5.18852	−	5.04747i	−0.215071	−	0.209224i
$583$	−19.0519	−	5.01128i	−0.789051	−	0.207546i
$584$	−8.67073	+	14.4005i	−0.358798	+	0.595899i
$585$	4.94618	−	1.49731i	0.204500	−	0.0619061i
$586$	3.40767	+	6.16093i	0.140769	+	0.254506i
$587$	2.51679	−	1.88569i	0.103879	−	0.0778306i	−0.546408	−	0.837519i	$-0.684005\pi$
$587$	2.51679	−	1.88569i	0.103879	−	0.0778306i	0.650287	+	0.759688i	$0.274649\pi$
$588$	−16.4289	+	64.8764i	−0.677518	+	2.67546i
$589$	−9.10767	−	15.1091i	−0.375275	−	0.622561i
$590$	−0.0121325	−	0.0479102i	−0.000499488	−	0.00197243i
$591$	−50.0441	−	40.4488i	−2.05854	−	1.66384i
$592$	0.0330215	+	0.0416313i	0.00135717	+	0.00171104i
$593$	24.3861	+	9.38666i	1.00142	+	0.385464i	0.803854	−	0.594826i	$-0.202779\pi$
$593$	24.3861	+	9.38666i	1.00142	+	0.385464i	0.197563	+	0.980290i	$0.436697\pi$
$594$	−3.29793	−	0.426478i	−0.135316	−	0.0174986i
$595$	−1.44634	+	8.20259i	−0.0592941	+	0.336273i
$596$	−0.247381	+	8.97453i	−0.0101331	+	0.367611i
$597$	22.6599	+	5.07821i	0.927410	+	0.207837i
$598$	11.3045	−	9.13699i	0.462274	−	0.373639i
$599$	18.1796	+	13.6209i	0.742796	+	0.556534i	0.902531	−	0.430626i	$-0.141707\pi$
$599$	18.1796	+	13.6209i	0.742796	+	0.556534i	−0.159734	+	0.987160i	$0.551064\pi$
$600$	3.43562	−	24.7759i	0.140259	−	1.01147i
$601$	11.7799	+	8.16801i	0.480513	+	0.333180i	0.785168	−	0.619282i	$-0.212576\pi$
$601$	11.7799	+	8.16801i	0.480513	+	0.333180i	−0.304655	+	0.952463i	$0.598541\pi$
$602$	−16.1567	−	10.7688i	−0.658499	−	0.438902i
$603$	28.3525	+	20.4405i	1.15460	+	0.832402i
$604$	−10.2598	−	2.10210i	−0.417464	−	0.0855332i
$605$	0.386304	−	2.45362i	0.0157055	−	0.0997536i
$606$	6.95014	+	2.52964i	0.282330	+	0.102760i
$607$	−4.54755	−	3.53950i	−0.184579	−	0.143664i	0.517708	−	0.855557i	$-0.326785\pi$
$607$	−4.54755	−	3.53950i	−0.184579	−	0.143664i	−0.702288	+	0.711893i	$0.747838\pi$
$608$	5.73190	−	21.0467i	0.232459	−	0.853557i
$609$	−33.8011	+	26.3085i	−1.36969	+	1.06607i
$610$	−0.586229	+	0.189287i	−0.0237357	+	0.00766401i
$611$	16.4128	+	3.99622i	0.663992	+	0.161670i
$612$	47.4982	−	6.14232i	1.92000	−	0.248289i
$613$	−0.339339	+	7.38303i	−0.0137058	+	0.298198i	0.980903	+	0.194498i	$0.0623078\pi$
$613$	−0.339339	+	7.38303i	−0.0137058	+	0.298198i	−0.994609	+	0.103700i	$0.966932\pi$
$614$	−0.136975	−	0.869998i	−0.00552786	−	0.0351103i
$615$	0.0285018	−	0.145913i	0.00114930	−	0.00588379i
$616$	0.385854	+	13.9981i	0.0155465	+	0.563998i
$617$	3.12802	+	0.463080i	0.125929	+	0.0186429i	0.209114	−	0.977891i	$-0.432942\pi$
$617$	3.12802	+	0.463080i	0.125929	+	0.0186429i	−0.0831850	+	0.996534i	$0.526509\pi$
$618$	−24.1420	+	4.48592i	−0.971132	+	0.180450i
$619$	−24.4602	−	9.93489i	−0.983140	−	0.399317i	−0.172595	−	0.984993i	$-0.555215\pi$
$619$	−24.4602	−	9.93489i	−0.983140	−	0.399317i	−0.810545	+	0.585676i	$0.800829\pi$
$620$	−1.92228	−	0.907146i	−0.0772007	−	0.0364319i
$621$	−18.8853	−	24.7291i	−0.757839	−	0.992345i
$622$	−11.3194	+	13.2410i	−0.453868	+	0.530918i
$623$	−48.4993	−	40.6958i	−1.94308	−	1.63044i
$624$	−19.8441	+	18.6074i	−0.794399	+	0.744892i
$625$	−5.38667	−	23.0423i	−0.215467	−	0.921694i
$626$	8.55347	−	4.62890i	0.341865	−	0.185008i
$627$	−19.4950	+	2.16756i	−0.778557	+	0.0865642i
$628$	−3.35981	−	1.81824i	−0.134071	−	0.0725557i
$629$	0.0328915	−	0.120536i	0.00131147	−	0.00480607i
$630$	2.78162	−	1.25073i	0.110823	−	0.0498301i
$631$	7.85828	−	5.66538i	0.312833	−	0.225535i	−0.417417	−	0.908715i	$-0.637064\pi$
$631$	7.85828	−	5.66538i	0.312833	−	0.225535i	0.730250	+	0.683180i	$0.239404\pi$
$632$	20.4348	−	0.751190i	0.812853	−	0.0298807i
$633$	−16.4347	−	31.0466i	−0.653221	−	1.23399i
$634$	0.283892	−	0.758243i	0.0112748	−	0.0301137i
$635$	2.19419	−	0.620458i	0.0870739	−	0.0246221i
$636$	−32.3421	−	47.5711i	−1.28245	−	1.88632i
$637$	−28.4780	+	45.3886i	−1.12834	+	1.79836i
$638$	−1.65106	+	2.24635i	−0.0653662	+	0.0889339i
$639$	50.6365	+	14.3186i	2.00315	+	0.566437i
$640$	−1.07304	−	3.22173i	−0.0424157	−	0.127350i
$641$	−2.34333	−	2.36495i	−0.0925559	−	0.0934101i	0.662532	−	0.749034i	$-0.269482\pi$
$641$	−2.34333	−	2.36495i	−0.0925559	−	0.0934101i	−0.755088	+	0.655624i	$0.772406\pi$
$642$	−3.63539	−	9.19182i	−0.143477	−	0.362772i
$643$	−13.9307	+	1.28328i	−0.549373	+	0.0506075i	−0.362858	−	0.931845i	$-0.618199\pi$
$643$	−13.9307	+	1.28328i	−0.549373	+	0.0506075i	−0.186515	+	0.982452i	$0.559719\pi$
$644$	−42.2875	+	44.2758i	−1.66636	+	1.74471i
$645$	−0.579125	−	6.98900i	−0.0228030	−	0.275192i
$646$	−12.2591	+	4.72578i	−0.482328	+	0.185933i
$647$	2.44032	−	29.4503i	0.0959390	−	1.15781i	−0.763233	−	0.646124i	$-0.776389\pi$
$647$	2.44032	−	29.4503i	0.0959390	−	1.15781i	0.859172	−	0.511688i	$-0.170979\pi$
$648$	2.84893	+	3.21120i	0.111917	+	0.126148i
$649$	0.256147	−	0.483885i	0.0100546	−	0.0189941i
$650$	4.07123	−	8.42570i	0.159687	−	0.330483i
$651$	6.03867	+	50.3272i	0.236674	+	1.97248i
$652$	4.57268	+	4.28772i	0.179080	+	0.167920i
$653$	4.60717	−	7.97984i	0.180292	−	0.312275i	−0.761688	−	0.647944i	$-0.775629\pi$
$653$	4.60717	−	7.97984i	0.180292	−	0.312275i	0.941980	+	0.335669i	$0.108962\pi$
$654$	9.89476	+	17.1382i	0.386916	+	0.670158i
$655$	0.0925514	−	0.395904i	0.00361628	−	0.0154692i
$656$	0.123509	+	0.452616i	0.00482222	+	0.0176717i
$657$	25.7828	+	31.3063i	1.00588	+	1.22138i
$658$	9.90873	+	1.09670i	0.386282	+	0.0427537i
$659$	−0.0243379	+	2.64940i	−0.000948070	+	0.103206i	0.998151	+	0.0607765i	$0.0193577\pi$
$659$	−0.0243379	+	2.64940i	−0.000948070	+	0.103206i	−0.999099	+	0.0424294i	$0.986490\pi$
$660$	−1.81041	+	1.51912i	−0.0704703	+	0.0591316i
$661$	3.64092	−	30.3440i	0.141615	−	1.18024i	−0.727668	−	0.685929i	$-0.759396\pi$
$661$	3.64092	−	30.3440i	0.141615	−	1.18024i	0.869283	−	0.494314i	$-0.164581\pi$
$662$	8.41218	+	5.38635i	0.326949	+	0.209347i
$663$	62.8873	+	11.6853i	2.44234	+	0.453821i
$664$	−9.34189	−	3.20708i	−0.362536	−	0.124459i
$665$	4.71052	−	3.67012i	0.182666	−	0.142321i
$666$	−0.0432714	+	0.0148551i	−0.00167673	+	0.000575623i
$667$	−25.8046	+	3.82018i	−0.999159	+	0.147918i
$668$	6.22849	+	35.3235i	0.240988	+	1.36671i
$669$	−1.07140	−	23.3106i	−0.0414229	−	0.901241i
$670$	−1.13174	+	0.231879i	−0.0437228	+	0.00895827i
$671$	−6.22411	−	2.79860i	−0.240279	−	0.108039i
$672$	−39.8430	+	48.3786i	−1.53698	+	1.86625i
$673$	−22.4866	+	21.8753i	−0.866794	+	0.843230i	−0.988792	−	0.149300i	$-0.952298\pi$
$673$	−22.4866	+	21.8753i	−0.866794	+	0.843230i	0.121998	+	0.992530i	$0.461070\pi$
$674$	2.13587	−	1.20712i	0.0822706	−	0.0464966i
$675$	−17.7898	−	9.20894i	−0.684731	−	0.354452i
$676$	−2.81801	+	1.32985i	−0.108385	+	0.0511481i
$677$	24.2305	−	1.33684i	0.931255	−	0.0513788i	0.416896	−	0.908954i	$-0.363118\pi$
$677$	24.2305	−	1.33684i	0.931255	−	0.0513788i	0.514359	+	0.857575i	$0.328030\pi$
$678$	−3.44829	+	9.75189i	−0.132431	+	0.374519i
$679$	14.0939	+	19.9328i	0.540876	+	0.764949i
$680$	−1.95586	+	2.76613i	−0.0750038	+	0.106076i
$681$	6.35986	+	17.9859i	0.243710	+	0.689223i
$682$	1.26952	+	3.04509i	0.0486124	+	0.116603i
$683$	20.3409	−	22.0961i	0.778322	−	0.845483i	−0.212984	−	0.977056i	$-0.568318\pi$
$683$	20.3409	−	22.0961i	0.778322	−	0.845483i	0.991307	+	0.131572i	$0.0420026\pi$
$684$	−28.2272	−	19.5514i	−1.07929	−	0.747567i
$685$	3.11574	+	3.38459i	0.119046	+	0.129319i
$686$	−6.58747	+	14.2980i	−0.251511	+	0.545899i
$687$	22.3285	+	20.1791i	0.851887	+	0.769881i
$688$	11.4157	+	18.9595i	0.435220	+	0.722823i
$689$	−12.9387	−	44.2017i	−0.492926	−	1.68395i
$690$	3.08524	+	0.284208i	0.117453	+	0.0108196i
$691$	−10.3160	+	8.98423i	−0.392440	+	0.341776i	−0.830350	−	0.557243i	$-0.811859\pi$
$691$	−10.3160	+	8.98423i	−0.392440	+	0.341776i	0.437910	+	0.899019i	$0.355719\pi$
$692$	7.49571	+	4.60759i	0.284944	+	0.175154i
$693$	32.1518	+	10.3815i	1.22135	+	0.394361i
$694$	1.33434	−	0.485661i	0.0506510	−	0.0184355i
$695$	0.966752	+	4.94923i	0.0366710	+	0.187735i
$696$	−17.0000	+	3.80978i	−0.644382	+	0.144409i
$697$	0.685540	−	0.864284i	0.0259667	−	0.0327371i
$698$	1.17700	−	0.694035i	0.0445502	−	0.0262696i
$699$	−27.9407	+	13.8187i	−1.05681	+	0.522673i
$700$	−12.4556	+	37.3969i	−0.470776	+	1.41347i
$701$	16.7290	−	24.6063i	0.631846	−	0.929365i	−0.368154	−	0.929765i	$-0.620010\pi$
$701$	16.7290	−	24.6063i	0.631846	−	0.929365i	1.00000		0.000399308i	$0.000127104\pi$
$702$	−3.12295	−	7.11960i	−0.117868	−	0.268712i
$703$	−0.0754134	+	0.0483406i	−0.00284427	+	0.00182320i
$704$	1.77700	−	4.05115i	0.0669731	−	0.152683i
$705$	1.91370	+	3.05007i	0.0720739	+	0.114872i
$706$	2.35518	+	0.173389i	0.0886384	+	0.00652557i
$707$	−21.4862	−	12.6697i	−0.808074	−	0.476492i
$708$	1.49199	−	0.574294i	0.0560724	−	0.0215833i
$709$	21.5635	−	5.25032i	0.809834	−	0.197180i	0.189869	−	0.981809i	$-0.439194\pi$
$709$	21.5635	−	5.25032i	0.809834	−	0.197180i	0.619965	+	0.784630i	$0.287147\pi$
$710$	−1.48171	+	0.910805i	−0.0556076	+	0.0341819i
$711$	14.7278	−	47.0874i	0.552335	−	1.76591i
$712$	−10.7755	−	23.3880i	−0.403830	−	0.876504i
$713$	−11.8789	+	28.4929i	−0.444867	+	1.06707i
$714$	37.6917	+	2.07951i	1.41058	+	0.0778237i
$715$	−1.75311	+	0.712050i	−0.0655625	+	0.0266292i
$716$	10.1991	−	6.53053i	0.381159	−	0.244057i
$717$	−8.40371	−	17.3921i	−0.313842	−	0.649518i
$718$	4.33341	+	0.159298i	0.161722	+	0.00594494i
$719$	−9.42126	+	6.27945i	−0.351354	+	0.234184i	−0.717791	−	0.696259i	$-0.754847\pi$
$719$	−9.42126	+	6.27945i	−0.351354	+	0.234184i	0.366437	+	0.930443i	$0.380578\pi$
$720$	−3.47565	−	0.0638614i	−0.129530	−	0.00237997i
$721$	82.8120			3.08408
$722$	8.79412	+	3.37494i	0.327283	+	0.125602i
$723$	−55.2868			−2.05614
$724$	14.7815	+	0.271595i	0.549352	+	0.0100938i
$725$	−13.9743	+	9.31415i	−0.518993	+	0.345919i
$726$	−11.2496	−	0.413539i	−0.417511	−	0.0153479i
$727$	16.4929	+	34.1333i	0.611689	+	1.26593i	0.946213	+	0.323545i	$0.104875\pi$
$727$	16.4929	+	34.1333i	0.611689	+	1.26593i	−0.334524	+	0.942387i	$0.608576\pi$
$728$	−27.5709	+	17.6537i	−1.02184	+	0.654290i
$729$	40.6297	−	16.5023i	1.50480	−	0.611198i
$730$	−1.33844	−	0.0738438i	−0.0495379	−	0.00273308i
$731$	20.0240	−	48.0300i	0.740615	−	1.77645i
$732$	−8.33853	−	18.0986i	−0.308201	−	0.668943i
$733$	−7.82506	+	25.0181i	−0.289025	+	0.924065i	0.690601	+	0.723236i	$0.257346\pi$
$733$	−7.82506	+	25.0181i	−0.289025	+	0.924065i	−0.979626	+	0.200829i	$0.935636\pi$
$734$	−4.68431	+	2.87944i	−0.172901	+	0.106282i
$735$	−11.0973	+	2.70200i	−0.409332	+	0.0996648i
$736$	−35.6213	+	13.7113i	−1.31302	+	0.505406i
$737$	−11.0239	−	6.50042i	−0.406072	−	0.239446i
$738$	−0.402852	−	0.0296580i	−0.0148292	−	0.00109173i
$739$	−0.0358527	−	0.0571424i	−0.00131886	−	0.00210202i	0.846413	−	0.532527i	$-0.178758\pi$
$739$	−0.0358527	−	0.0571424i	−0.00131886	−	0.00210202i	−0.847732	+	0.530425i	$0.822032\pi$
$740$	−0.00433535	+	0.00988360i	−0.000159371	+	0.000363328i
$741$	−27.8513	−	36.4319i	−1.02314	−	1.33836i
$742$	−10.9184	−	24.8915i	−0.400829	−	0.913797i
$743$	−19.7350	+	29.0277i	−0.724007	+	1.06492i	0.270749	+	0.962650i	$0.412729\pi$
$743$	−19.7350	+	29.0277i	−0.724007	+	1.06492i	−0.994756	+	0.102273i	$0.967388\pi$
$744$	−6.51483	+	19.5603i	−0.238845	+	0.717115i
$745$	−1.37342	+	0.679256i	−0.0503181	+	0.0248860i
$746$	−5.77008	+	3.40241i	−0.211257	+	0.124571i
$747$	−14.8092	+	18.6705i	−0.541841	+	0.683117i
$748$	−17.1117	+	3.83483i	−0.625667	+	0.140215i
$749$	6.39081	+	32.7174i	0.233515	+	1.19547i
$750$	3.78296	−	1.37689i	0.138134	−	0.0502768i
$751$	14.6673	+	4.73591i	0.535216	+	0.172816i	0.562478	−	0.826813i	$-0.309848\pi$
$751$	14.6673	+	4.73591i	0.535216	+	0.172816i	−0.0272615	+	0.999628i	$0.508679\pi$
$752$	−9.68026	−	5.95043i	−0.353003	−	0.216990i
$753$	−24.4558	+	21.2986i	−0.891219	+	0.776163i
$754$	−6.49022	−	0.597871i	−0.236360	−	0.0217732i
$755$	−0.502120	−	1.71536i	−0.0182740	−	0.0624284i
$756$	16.8919	+	28.0545i	0.614353	+	1.02033i
$757$	−1.27074	−	1.14841i	−0.0461858	−	0.0417398i	0.647077	−	0.762425i	$-0.275991\pi$
$757$	−1.27074	−	1.14841i	−0.0461858	−	0.0417398i	−0.693263	+	0.720685i	$0.743827\pi$
$758$	−5.66638	+	12.2988i	−0.205812	+	0.446711i
$759$	23.2462	+	25.2521i	0.843784	+	0.916594i
$760$	2.36977	−	0.532320i	0.0859605	−	0.0193093i
$761$	7.93099	−	8.61535i	0.287498	−	0.312306i	−0.575213	−	0.818004i	$-0.695081\pi$
$761$	7.93099	−	8.61535i	0.287498	−	0.312306i	0.862711	+	0.505698i	$0.168765\pi$
$762$	−3.97672	−	9.53863i	−0.144061	−	0.345548i
$763$	−22.2493	−	62.9220i	−0.805480	−	2.27793i
$764$	−17.1985	+	24.3234i	−0.622220	+	0.879991i
$765$	4.71896	+	6.67392i	0.170614	+	0.241296i
$766$	3.11358	−	8.80532i	0.112498	−	0.318149i
$767$	1.27805	−	0.0705122i	0.0461478	−	0.00254605i
$768$	−0.599429	+	0.282878i	−0.0216300	+	0.0102075i
$769$	−0.302466	−	0.156572i	−0.0109072	−	0.00564613i	0.454248	−	0.890875i	$-0.349908\pi$
$769$	−0.302466	−	0.156572i	−0.0109072	−	0.00564613i	−0.465155	+	0.885229i	$0.654002\pi$
$770$	−0.972182	+	0.549445i	−0.0350350	+	0.0198006i
$771$	21.5027	−	20.9182i	0.774402	−	0.753350i
$772$	8.77554	−	10.6555i	0.315839	−	0.383502i
$773$	43.2589	+	19.4509i	1.55591	+	0.699599i	0.992000	−	0.126234i	$-0.0402891\pi$
$773$	43.2589	+	19.4509i	1.55591	+	0.699599i	0.563914	+	0.825834i	$0.309295\pi$
$774$	−18.6666	+	3.82455i	−0.670957	+	0.137471i
$775$	0.912480	+	19.8529i	0.0327772	+	0.713137i
$776$	1.72420	+	9.77845i	0.0618953	+	0.351026i
$777$	0.254595	−	0.0376909i	0.00913354	−	0.00135215i
$778$	−14.7097	+	5.04983i	−0.527367	+	0.181045i
$779$	−0.780046	+	0.130567i	−0.0279480	+	0.00467805i
$780$	−5.22585	−	1.79404i	−0.187115	−	0.0642368i
$781$	−18.9432	−	3.51991i	−0.677840	−	0.125952i
$782$	19.3610	+	12.3969i	0.692346	+	0.443312i
$783$	−1.66220	+	13.8530i	−0.0594021	+	0.495066i
$784$	27.6108	−	23.1682i	0.986099	−	0.827435i
$785$	0.00598896	−	0.651951i	0.000213755	−	0.0232691i
$786$	−1.83150	−	0.202710i	−0.0653273	−	0.00723043i
$787$	−3.45244	−	4.19207i	−0.123066	−	0.149431i	0.706759	−	0.707454i	$-0.250157\pi$
$787$	−3.45244	−	4.19207i	−0.123066	−	0.149431i	−0.829825	+	0.558023i	$0.811560\pi$
$788$	10.8574	+	39.7885i	0.386779	+	1.41741i
$789$	−8.66395	+	37.0614i	−0.308445	+	1.31942i
$790$	0.815340	+	1.41221i	0.0290085	+	0.0502442i
$791$	17.4418	−	30.2101i	0.620160	−	1.07415i
$792$	10.0245	+	9.39975i	0.356204	+	0.334006i
$793$	−1.90073	−	15.8410i	−0.0674969	−	0.562530i
$794$	1.96882	−	4.07461i	0.0698707	−	0.144602i
$795$	4.59300	−	8.67659i	0.162897	−	0.307727i
$796$	−9.87793	−	11.1340i	−0.350114	−	0.394635i
$797$	2.48203	−	29.9536i	0.0879179	−	1.06101i	−0.799691	−	0.600412i	$-0.795003\pi$
$797$	2.48203	−	29.9536i	0.0879179	−	1.06101i	0.887609	−	0.460599i	$-0.152365\pi$
$798$	−19.0585	−	19.2152i	−0.674665	−	0.680212i
$799$	2.20633	+	26.6265i	0.0780544	+	0.941976i
$800$	−16.9722	+	17.7702i	−0.600057	+	0.628270i
$801$	−61.8681	+	5.69921i	−2.18600	+	0.201372i
$802$	1.88130	+	4.75672i	0.0664309	+	0.167966i
$803$	−10.4520	−	10.5484i	−0.368842	−	0.372246i
$804$	−11.8087	−	35.4547i	−0.416460	−	1.25039i
$805$	−10.0547	−	2.84321i	−0.354383	−	0.100210i
$806$	−4.56793	+	6.21489i	−0.160898	+	0.218910i
$807$	−42.7580	+	68.1481i	−1.50515	+	2.39893i
$808$	−5.70411	−	8.39003i	−0.200670	−	0.295160i
$809$	−35.2261	+	9.96100i	−1.23848	+	0.350210i	−0.827517	−	0.561440i	$-0.810248\pi$
$809$	−35.2261	+	9.96100i	−1.23848	+	0.350210i	−0.410967	+	0.911650i	$0.634809\pi$
$810$	−0.120034	+	0.320598i	−0.00421758	+	0.0112646i
$811$	10.8006	+	20.4034i	0.379262	+	0.716460i	0.997584	−	0.0694644i	$-0.0221290\pi$
$811$	10.8006	+	20.4034i	0.379262	+	0.716460i	−0.618323	+	0.785924i	$0.712188\pi$
$812$	27.4353	−	1.00853i	0.962790	−	0.0353925i
$813$	43.2804	−	31.2027i	1.51791	−	1.09433i
$814$	0.0152780	−	0.00686957i	0.000535493	−	0.000240778i
$815$	−0.281629	+	1.03207i	−0.00986502	+	0.0361518i
$816$	−37.8404	−	20.4782i	−1.32468	−	0.716880i
$817$	−33.7313	+	15.9388i	−1.18011	+	0.557627i
$818$	15.0588	−	8.14940i	0.526518	−	0.284937i
$819$	17.9807	+	76.9152i	0.628296	+	2.68763i
$820$	−0.0695122	+	0.0651802i	−0.00242747	+	0.00227619i
$821$	12.4391	+	10.4377i	0.434128	+	0.364277i	0.833507	−	0.552509i	$-0.186330\pi$
$821$	12.4391	+	10.4377i	0.434128	+	0.364277i	−0.399378	+	0.916786i	$0.630774\pi$
$822$	13.5480	−	15.8480i	0.472542	−	0.552761i
$823$	2.25203	+	2.94891i	0.0785010	+	0.102792i	0.832336	−	0.554271i	$-0.187003\pi$
$823$	2.25203	+	2.94891i	0.0785010	+	0.102792i	−0.753835	+	0.657064i	$0.771798\pi$
$824$	30.4611	+	14.3749i	1.06116	+	0.500775i
$825$	20.4726	+	8.31523i	0.712763	+	0.289499i
$826$	0.742695	−	0.138003i	0.0258417	−	0.00480175i
$827$	−30.9867	−	4.58735i	−1.07751	−	0.159518i	−0.415935	−	0.909394i	$-0.636546\pi$
$827$	−30.9867	−	4.58735i	−1.07751	−	0.159518i	−0.661578	+	0.749877i	$0.730113\pi$
$828$	1.65555	+	60.0604i	0.0575345	+	2.08724i
$829$	−4.86574	+	24.9099i	−0.168994	+	0.865155i	0.796482	+	0.604662i	$0.206692\pi$
$829$	−4.86574	+	24.9099i	−0.168994	+	0.865155i	−0.965476	+	0.260493i	$0.916115\pi$
$830$	−0.122501	−	0.778065i	−0.00425207	−	0.0270070i
$831$	4.12357	−	89.7169i	0.143045	−	3.11225i
$832$	10.2569	−	1.32638i	0.355592	−	0.0459841i
$833$	−82.3435	−	20.0491i	−2.85303	−	0.694662i
$834$	21.7490	−	7.02254i	0.753107	−	0.243171i
$835$	−4.83068	+	3.75987i	−0.167173	+	0.130116i
$836$	10.9484	+	6.18046i	0.378658	+	0.213756i
$837$	13.0297	+	10.1414i	0.450371	+	0.350538i
$838$	−14.0937	−	5.12969i	−0.486859	−	0.177202i
$839$	5.73730	−	36.4405i	0.198073	−	1.25807i	−0.662625	−	0.748951i	$-0.730558\pi$
$839$	5.73730	−	36.4405i	0.198073	−	1.25807i	0.860699	−	0.509114i	$-0.170027\pi$
$840$	−6.83641	−	1.40070i	−0.235879	−	0.0483286i
$841$	−14.0357	−	10.1189i	−0.483989	−	0.348929i
$842$	8.77526	+	5.84888i	0.302415	+	0.201566i
$843$	45.3490	+	31.4443i	1.56190	+	1.08300i
$844$	−3.09259	+	22.3022i	−0.106451	+	0.767672i
$845$	−0.425590	−	0.318870i	−0.0146407	−	0.0109695i
$846$	7.60864	−	6.14980i	0.261591	−	0.211434i
$847$	37.0458	+	8.30216i	1.27291	+	0.285266i
$848$	−0.853651	+	30.9689i	−0.0293145	+	1.06348i
$849$	−5.34167	+	30.2941i	−0.183326	+	1.03969i
$850$	14.6784	+	1.89817i	0.503466	+	0.0651067i
$851$	0.146280	+	0.0563058i	0.00501441	+	0.00193014i
$852$	−34.9626	−	44.0785i	−1.19780	−	1.51011i
$853$	−35.1597	−	28.4183i	−1.20384	−	0.973025i	−0.203863	−	0.978999i	$-0.565350\pi$
$853$	−35.1597	−	28.4183i	−1.20384	−	0.973025i	−0.999982	+	0.00597467i	$0.998098\pi$
$854$	−2.31145	−	9.12771i	−0.0790962	−	0.312344i
$855$	0.695227	−	5.81869i	0.0237763	−	0.198995i
$856$	−3.32849	+	13.1439i	−0.113766	+	0.449250i
$857$	9.19446	−	6.88888i	0.314077	−	0.235320i	−0.430916	−	0.902392i	$-0.641810\pi$
$857$	9.19446	−	6.88888i	0.314077	−	0.235320i	0.744993	+	0.667072i	$0.232453\pi$
$858$	4.15071	+	7.50434i	0.141703	+	0.256194i
$859$	−4.82032	+	1.45921i	−0.164467	+	0.0497875i	−0.370897	−	0.928674i	$-0.620950\pi$
$859$	−4.82032	+	1.45921i	−0.164467	+	0.0497875i	0.206430	+	0.978461i	$0.433815\pi$
$860$	−2.31862	+	3.85082i	−0.0790644	+	0.131312i
$861$	2.19764	+	0.578050i	0.0748953	+	0.0196999i
$862$	−7.92918	−	7.71362i	−0.270069	−	0.262727i
$863$	−10.7740	+	1.19246i	−0.366750	+	0.0405919i	−0.291495	−	0.956572i	$-0.594153\pi$
$863$	−10.7740	+	1.19246i	−0.366750	+	0.0405919i	−0.0752552	+	0.997164i	$0.523977\pi$
$864$	2.05936	+	20.3111i	0.0700608	+	0.690999i
$865$	−0.0964890	+	1.49850i	−0.00328072	+	0.0509505i
$866$	−3.86394	+	7.63534i	−0.131302	+	0.259460i
$867$	7.50513	+	54.1231i	0.254888	+	1.83812i
$868$	15.7248	−	28.4298i	0.533733	−	0.964970i
$869$	−3.78829	+	17.6629i	−0.128509	+	0.599172i
$870$	−0.902759	−	1.05601i	−0.0306064	−	0.0358022i
$871$	−0.274838	−	29.9186i	−0.00931253	−	1.01375i
$872$	2.73826	−	27.0070i	0.0927291	−	0.914572i
$873$	23.6299	+	3.94314i	0.799752	+	0.133455i
$874$	−4.34696	−	15.8988i	−0.147038	−	0.537784i
$875$	−13.3916	+	2.23466i	−0.452719	+	0.0755454i
$876$	−2.78627	−	43.2716i	−0.0941394	−	1.46201i
$877$	−2.26756	−	0.969906i	−0.0765701	−	0.0327514i	0.354640	−	0.935003i	$-0.384603\pi$
$877$	−2.26756	−	0.969906i	−0.0765701	−	0.0327514i	−0.431210	+	0.902251i	$0.641913\pi$
$878$	−0.224063	+	0.226131i	−0.00756177	+	0.00763155i
$879$	−34.8397	−	17.2308i	−1.17511	−	0.581181i
$880$	1.26938	−	0.0934518i	0.0427907	−	0.00315026i
$881$	8.47896	+	11.5360i	0.285663	+	0.388659i	0.924812	−	0.380424i	$-0.124222\pi$
$881$	8.47896	+	11.5360i	0.285663	+	0.388659i	−0.639149	+	0.769083i	$0.720713\pi$
$882$	10.8812	+	29.0624i	0.366389	+	0.978581i
$883$	27.1564	−	30.6096i	0.913886	−	1.03010i	−0.0855442	−	0.996334i	$-0.527263\pi$
$883$	27.1564	−	30.6096i	0.913886	−	1.03010i	0.999430	−	0.0337620i	$-0.0107488\pi$
$884$	−28.3164	−	29.6478i	−0.952385	−	0.997164i
$885$	0.205751	+	0.179188i	0.00691623	+	0.00602335i
$886$	−4.66900	−	14.9276i	−0.156858	−	0.501504i
$887$	14.6352	−	13.2263i	0.491401	−	0.444097i	−0.386959	−	0.922097i	$-0.626474\pi$
$887$	14.6352	−	13.2263i	0.491401	−	0.444097i	0.878360	+	0.478000i	$0.158638\pi$
$888$	0.100191	+	0.0303299i	0.00336220	+	0.00101780i
$889$	7.30888	+	34.0776i	0.245132	+	1.14293i
$890$	1.24636	−	1.63203i	0.0417781	−	0.0547059i
$891$	−3.36785	+	1.74337i	−0.112827	+	0.0584052i
$892$	−8.18059	+	12.5213i	−0.273906	+	0.419245i
$893$	11.6183	−	15.2293i	0.388792	−	0.509628i
$894$	3.79814	+	5.81348i	0.127029	+	0.194432i
$895$	1.79937	+	1.01694i	0.0601464	+	0.0339927i
$896$	50.1952	−	13.2030i	1.67691	−	0.441081i
$897$	−22.5428	+	77.0116i	−0.752683	+	2.57134i
$898$	2.98396	−	7.54472i	0.0995761	−	0.251771i
$899$	12.7269	−	5.44368i	0.424465	−	0.181557i
$900$	17.4659	+	34.5135i	0.582195	+	1.15045i
$901$	59.8626	−	41.5078i	1.99431	−	1.38283i
$902$	0.147877	−	0.00271709i	0.00492378	−	9.04693e-5i
$903$	107.173	−	1.96919i	3.56649	−	0.0655305i
$904$	11.6597	−	8.08467i	0.387797	−	0.268892i
$905$	1.13926	+	2.25125i	0.0378704	+	0.0748339i
$906$	−7.44784	+	3.18567i	−0.247438	+	0.105837i
$907$	−9.73982	+	24.6264i	−0.323406	+	0.817707i	0.673507	+	0.739181i	$0.264787\pi$
$907$	−9.73982	+	24.6264i	−0.323406	+	0.817707i	−0.996912	+	0.0785256i	$0.974979\pi$
$908$	3.43512	−	11.7352i	0.113999	−	0.389446i
$909$	−23.6729	+	6.22674i	−0.785180	+	0.206528i
$910$	−2.27286	−	1.28455i	−0.0753446	−	0.0425823i
$911$	−14.2464	−	21.8057i	−0.472003	−	0.722455i	0.519222	−	0.854639i	$-0.326222\pi$
$911$	−14.2464	−	21.8057i	−0.472003	−	0.722455i	−0.991225	+	0.132185i	$0.957801\pi$
$912$	10.2982	+	29.0775i	0.341007	+	0.962852i
$913$	4.77241	−	7.30472i	0.157944	−	0.241751i
$914$	15.7150	−	8.13490i	0.519806	−	0.269079i
$915$	2.06410	−	2.70281i	0.0682369	−	0.0893522i
$916$	−4.04528	−	18.8611i	−0.133660	−	0.623188i
$917$	5.94786	+	1.80053i	0.196416	+	0.0594589i
$918$	9.12287	−	8.24467i	0.301100	−	0.272115i
$919$	2.88806	+	9.23364i	0.0952683	+	0.304590i	0.989810	−	0.142395i	$-0.0454803\pi$
$919$	2.88806	+	9.23364i	0.0952683	+	0.304590i	−0.894542	+	0.446985i	$0.852498\pi$
$920$	−3.20493	−	2.79118i	−0.105664	−	0.0920224i
$921$	3.35813	+	3.51602i	0.110654	+	0.115857i
$922$	4.82441	−	5.43788i	0.158883	−	0.179087i
$923$	−15.7946	−	42.1854i	−0.519884	−	1.38855i
$924$	−21.3932	−	29.1064i	−0.703783	−	0.957532i
$925$	0.100637	−	0.00740893i	0.00330893	−	0.000243604i
$926$	16.8936	+	8.35512i	0.555157	+	0.274566i
$927$	57.1998	−	57.7277i	1.87869	−	1.89603i
$928$	15.7361	+	6.73083i	0.516564	+	0.220950i
$929$	−3.37706	−	52.4467i	−0.110798	−	1.72072i	−0.561019	−	0.827803i	$-0.689590\pi$
$929$	−3.37706	−	52.4467i	−0.110798	−	1.72072i	0.450221	−	0.892917i	$-0.351345\pi$
$930$	−1.62166	+	0.270608i	−0.0531764	+	0.00887357i
$931$	34.1866	+	50.2302i	1.12042	+	1.64623i
$932$	19.7068	+	3.28848i	0.645516	+	0.107718i
$933$	9.70081	−	95.6775i	0.317590	−	3.13234i
$934$	−0.00271030	−	0.295040i	−8.86837e−5	−	0.00965401i
$935$	−1.94470	−	2.27484i	−0.0635986	−	0.0743952i
$936$	−6.73743	+	31.4132i	−0.220220	+	1.02677i
$937$	7.30024	−	13.1986i	0.238488	−	0.431178i	−0.728848	−	0.684676i	$-0.759944\pi$
$937$	7.30024	−	13.1986i	0.238488	−	0.431178i	0.967336	+	0.253498i	$0.0815811\pi$
$938$	−2.42534	−	17.4902i	−0.0791900	−	0.571077i
$939$	−24.2434	+	47.9062i	−0.791152	+	1.56336i
$940$	0.148299	−	2.30312i	0.00483697	−	0.0751195i
$941$	5.03285	+	49.6382i	0.164066	+	1.61816i	0.661011	+	0.750376i	$0.270128\pi$
$941$	5.03285	+	49.6382i	0.164066	+	1.61816i	−0.496944	+	0.867782i	$0.665545\pi$
$942$	−2.93695	+	0.325061i	−0.0956909	+	0.0105911i
$943$	0.991970	+	0.965004i	0.0323030	+	0.0314248i
$944$	−0.832686	−	0.219024i	−0.0271016	−	0.00712861i
$945$	−2.88284	+	4.78788i	−0.0937787	+	0.155750i
$946$	6.67745	−	2.02140i	0.217103	−	0.0657213i
$947$	15.4999	+	28.0232i	0.503679	+	0.910633i	0.999118	+	0.0419900i	$0.0133698\pi$
$947$	15.4999	+	28.0232i	0.503679	+	0.910633i	−0.495439	+	0.868643i	$0.664993\pi$
$948$	−42.2143	+	31.6287i	−1.37106	+	1.02725i
$949$	8.52253	−	33.6547i	0.276653	−	1.09248i
$950$	−6.89916	−	8.06222i	−0.223838	−	0.261573i
$951$	1.09725	+	4.33293i	0.0355807	+	0.140505i
$952$	−40.2711	−	32.5497i	−1.30519	−	1.05494i
$953$	−20.1994	−	25.4661i	−0.654323	−	0.824928i	0.338940	−	0.940808i	$-0.389932\pi$
$953$	−20.1994	−	25.4661i	−0.654323	−	0.824928i	−0.993263	+	0.115880i	$0.963031\pi$
$954$	−24.8933	−	9.58188i	−0.805950	−	0.310225i
$955$	−5.04201	−	0.652018i	−0.163156	−	0.0210988i
$956$	−2.14987	+	12.1925i	−0.0695318	+	0.394335i
$957$	0.424075	−	15.3847i	0.0137084	−	0.497315i
$958$	19.8804	+	4.45530i	0.642307	+	0.143944i
$959$	−54.6857	+	44.2005i	−1.76589	+	1.42731i
$960$	1.76426	+	1.32186i	0.0569413	+	0.0426628i
$961$	−2.00799	+	14.4806i	−0.0647740	+	0.467116i
$962$	0.0321832	+	0.0223154i	0.00103763	+	0.000719476i
$963$	27.2213	+	18.1435i	0.877195	+	0.584667i
$964$	28.7449	+	20.7234i	0.925809	+	0.667456i
$965$	2.30790	+	0.472860i	0.0742939	+	0.0152219i
$966$	−7.36524	+	46.7804i	−0.236973	+	1.50513i
$967$	−24.9284	−	9.07321i	−0.801644	−	0.291775i	−0.0914766	−	0.995807i	$-0.529159\pi$
$967$	−24.9284	−	9.07321i	−0.801644	−	0.291775i	−0.710168	+	0.704033i	$0.751381\pi$
$968$	12.1856	+	9.48442i	0.391660	+	0.304841i
$969$	40.7499	−	60.0024i	1.30907	−	1.92755i
$970$	−0.624853	+	0.486343i	−0.0200628	+	0.0156155i
$971$	−15.5852	+	5.03230i	−0.500153	+	0.161494i	−0.546546	−	0.837429i	$-0.684058\pi$
$971$	−15.5852	+	5.03230i	−0.500153	+	0.161494i	0.0463932	+	0.998923i	$0.485227\pi$
$972$	−31.6191	−	7.69867i	−1.01418	−	0.246935i
$973$	−76.4406	+	9.88506i	−2.45057	+	0.316900i
$974$	−0.0948177	+	2.06296i	−0.00303815	+	0.0661014i
$975$	8.03454	+	51.0314i	0.257311	+	1.63431i
$976$	−2.05746	+	10.5331i	−0.0658577	+	0.337155i
$977$	0.741631	+	26.9050i	0.0237269	+	0.860767i	0.914089	+	0.405514i	$0.132907\pi$
$977$	0.741631	+	26.9050i	0.0237269	+	0.860767i	−0.890362	+	0.455253i	$0.849549\pi$
$978$	4.79626	+	0.710051i	0.153367	+	0.0227049i
$979$	22.3659	−	4.15591i	0.714818	−	0.132823i
$980$	6.78257	+	2.75484i	0.216661	+	0.0880001i
$981$	−59.2305	−	27.9515i	−1.89108	−	0.892424i
$982$	5.10376	+	6.68308i	0.162868	+	0.213266i
$983$	5.66363	−	6.62510i	0.180642	−	0.211308i	−0.662408	−	0.749143i	$-0.730465\pi$
$983$	5.66363	−	6.62510i	0.180642	−	0.211308i	0.843050	+	0.537836i	$0.180758\pi$
$984$	0.708025	+	0.594104i	0.0225710	+	0.0189393i
$985$	−5.13456	+	4.81457i	−0.163601	+	0.153405i
$986$	−2.34663	−	10.0381i	−0.0747318	−	0.319677i
$987$	−48.4025	+	26.1941i	−1.54067	+	0.833769i
$988$	0.824576	+	29.3814i	0.0262332	+	0.934747i
$989$	57.4129	+	31.0703i	1.82562	+	0.987978i
$990$	−0.288490	+	1.05721i	−0.00916883	+	0.0336005i
$991$	29.1183	−	13.0927i	0.924973	−	0.415904i	0.109032	−	0.994038i	$-0.465225\pi$
$991$	29.1183	−	13.0927i	0.924973	−	0.415904i	0.815941	+	0.578134i	$0.196219\pi$
$992$	16.4295	−	11.8448i	0.521638	−	0.376071i
$993$	−55.1070	+	2.02575i	−1.74877	+	0.0642853i
$994$	−12.4373	−	23.4952i	−0.394488	−	0.745224i
$995$	0.890688	−	2.37892i	0.0282367	−	0.0754169i
$996$	24.5172	−	6.93281i	0.776858	−	0.219675i
$997$	−21.0027	−	30.8924i	−0.665163	−	0.978371i	−0.999357	−	0.0358663i	$-0.988581\pi$
$997$	−21.0027	−	30.8924i	−0.665163	−	0.978371i	0.334194	−	0.942504i	$-0.391536\pi$
$998$	−3.38546	+	5.39578i	−0.107165	+	0.170800i
$999$	0.0496505	−	0.0675519i	0.00157087	−	0.00213725i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	361.2.k.a.4.14	✓	3348
361.271	even	171	inner	361.2.k.a.271.14	yes	3348

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
361.2.k.a.4.14	✓	3348	1.1	even	1	trivial
361.2.k.a.271.14	yes	3348	361.271	even	171	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 361 = 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	361.k (of order \(171\), degree \(108\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.495679 - 0.00910759i) q^{2} +(2.27739 - 1.51792i) q^{3} +(-1.75304 - 0.0644421i) q^{4} +(-0.130251 - 0.269563i) q^{5} +(-1.14268 + 0.731660i) q^{6} +(4.23959 - 1.72197i) q^{7} +(1.85838 + 0.102529i) q^{8} +(1.72799 - 4.14479i) q^{9} +(0.0621075 + 0.134803i) q^{10} +(-0.490821 + 1.56924i) q^{11} +(-4.09016 + 2.51421i) q^{12} +(-3.73488 + 0.909376i) q^{13} +(-2.11716 + 0.814934i) q^{14} +(-0.705806 - 0.416188i) q^{15} +(2.57874 + 0.189848i) q^{16} +(-3.23130 - 5.15008i) q^{17} +(-0.894278 + 2.03875i) q^{18} +(-0.754771 + 4.29305i) q^{19} +(0.210963 + 0.480947i) q^{20} +(7.04137 - 10.3570i) q^{21} +(0.257582 - 0.773371i) q^{22} +(6.83679 - 3.38130i) q^{23} +(4.38787 - 2.58737i) q^{24} +(3.05148 - 3.84710i) q^{25} +(1.85959 - 0.416743i) q^{26} +(-0.782091 - 4.00387i) q^{27} +(-7.54312 + 2.74547i) q^{28} +(-3.25463 - 1.05089i) q^{29} +(0.346063 + 0.212724i) q^{30} +(-3.05211 + 2.65809i) q^{31} +(-4.98321 - 0.459047i) q^{32} +(1.26420 + 4.31880i) q^{33} +(1.55478 + 2.58222i) q^{34} +(-1.01639 - 0.918548i) q^{35} +(-3.29633 + 7.15461i) q^{36} +(0.0139183 + 0.0151193i) q^{37} +(0.413224 - 2.12110i) q^{38} +(-7.12541 + 7.74026i) q^{39} +(-0.214417 - 0.514303i) q^{40} +(0.0604888 + 0.171065i) q^{41} +(-3.58459 + 5.06960i) q^{42} +(4.94134 + 6.98843i) q^{43} +(0.961553 - 2.71931i) q^{44} +(-1.34235 + 0.0740597i) q^{45} +(-3.41965 + 1.61377i) q^{46} +(-3.90259 - 2.02018i) q^{47} +(6.16097 - 3.48198i) q^{48} +(9.99148 - 9.71986i) q^{49} +(-1.54759 + 1.87914i) q^{50} +(-15.1763 - 6.82386i) q^{51} +(6.60598 - 1.35348i) q^{52} +(0.550110 + 11.9688i) q^{53} +(0.351200 + 1.99176i) q^{54} +(0.486939 - 0.0720878i) q^{55} +(8.05531 - 2.76539i) q^{56} +(4.79761 + 10.9226i) q^{57} +(1.60368 + 0.550545i) q^{58} +(-0.327382 - 0.0608322i) q^{59} +(1.21048 + 0.775076i) q^{60} +(-0.494467 + 4.12097i) q^{61} +(1.53708 - 1.28976i) q^{62} +(0.188756 - 20.5478i) q^{63} +(-2.67417 - 0.295977i) q^{64} +(0.731605 + 0.888338i) q^{65} +(-0.587303 - 2.15225i) q^{66} +(-1.77181 + 7.57918i) q^{67} +(5.33270 + 9.23650i) q^{68} +(10.4375 - 18.0782i) q^{69} +(0.495437 + 0.464562i) q^{70} +(1.39605 + 11.6349i) q^{71} +(3.63622 - 7.52541i) q^{72} +(-4.22537 + 7.98211i) q^{73} +(-0.00676133 - 0.00762111i) q^{74} +(1.10980 - 13.3932i) q^{75} +(1.59979 - 7.47724i) q^{76} +(0.621313 + 7.49814i) q^{77} +(3.60241 - 3.77179i) q^{78} +(10.9404 - 1.00782i) q^{79} +(-0.284707 - 0.719861i) q^{80} +(1.62341 + 1.63840i) q^{81} +(-0.0284251 - 0.0853442i) q^{82} +(-5.10658 - 1.44400i) q^{83} +(-13.0112 + 17.7024i) q^{84} +(-0.967391 + 1.54184i) q^{85} +(-2.38567 - 3.50902i) q^{86} +(-9.00723 + 2.54700i) q^{87} +(-1.07302 + 2.86592i) q^{88} +(-6.47300 - 12.2281i) q^{89} +(0.666051 - 0.0244842i) q^{90} +(-14.2685 + 10.2868i) q^{91} +(-12.2030 + 5.48695i) q^{92} +(-2.91607 + 10.6864i) q^{93} +(1.91603 + 1.03691i) q^{94} +(1.25556 - 0.355715i) q^{95} +(-12.0455 + 6.51870i) q^{96} +(1.21441 + 5.19482i) q^{97} +(-5.04109 + 4.72693i) q^{98} +(5.65605 + 4.74599i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3348 q - 108 q^{2} - 111 q^{3} - 114 q^{4} - 108 q^{5} - 117 q^{6} - 111 q^{7} - 120 q^{8} - 117 q^{9} - 123 q^{10} - 111 q^{11} - 117 q^{12} - 111 q^{13} - 111 q^{14} - 117 q^{15} - 96 q^{16} - 3 q^{17}+ \cdots - 123 q^{99}+O(q^{100}) \) 3348 * q - 108 * q^2 - 111 * q^3 - 114 * q^4 - 108 * q^5 - 117 * q^6 - 111 * q^7 - 120 * q^8 - 117 * q^9 - 123 * q^10 - 111 * q^11 - 117 * q^12 - 111 * q^13 - 111 * q^14 - 117 * q^15 - 96 * q^16 - 3 * q^17 - 108 * q^18 - 102 * q^19 - 132 * q^20 - 114 * q^21 - 120 * q^23 - 129 * q^24 - 114 * q^25 - 105 * q^26 - 63 * q^27 - 120 * q^28 - 111 * q^29 - 90 * q^30 - 123 * q^31 - 123 * q^32 + 9 * q^33 - 114 * q^34 - 120 * q^35 - 90 * q^36 - 114 * q^37 - 42 * q^38 - 126 * q^39 - 114 * q^40 - 135 * q^41 - 111 * q^42 + 3 * q^43 - 123 * q^44 - 84 * q^45 - 96 * q^46 - 111 * q^47 + 516 * q^48 - 24 * q^49 - 99 * q^50 - 117 * q^51 - 129 * q^52 - 111 * q^53 + 483 * q^54 - 132 * q^55 - 108 * q^56 - 138 * q^57 - 174 * q^58 - 126 * q^59 - 108 * q^60 - 102 * q^61 - 102 * q^62 - 126 * q^63 + 6 * q^64 - 102 * q^65 - 105 * q^66 - 84 * q^67 - 12 * q^68 + 411 * q^69 + 351 * q^70 - 108 * q^71 - 102 * q^72 - 102 * q^73 - 15 * q^74 - 144 * q^75 - 150 * q^76 - 162 * q^77 - 129 * q^78 - 75 * q^79 - 117 * q^80 - 120 * q^81 - 60 * q^82 - 90 * q^83 - 117 * q^84 - 114 * q^85 + 888 * q^86 - 63 * q^87 - 123 * q^88 - 102 * q^89 + 894 * q^90 - 15 * q^91 - 156 * q^92 - 123 * q^93 - 132 * q^94 + 75 * q^95 - 276 * q^96 - 132 * q^97 - 105 * q^98 - 123 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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